{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaptive Rejection Sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import beta\n",
    "from scipy.integrate import quad\n",
    "from numpy.random import rand, seed, random_sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, b = 3, 2\n",
    "p = beta(a=a, b=b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(3141592653)\n",
    "z0 = p.rvs(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 400
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xrange = np.linspace(0, 0.9999, 100)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax2 = ax.twinx()\n",
    "l1 = ax.plot(xrange, p.pdf(xrange), label=\"pdf\")\n",
    "l2 = ax2.plot(xrange, p.logpdf(xrange), c=\"tab:orange\", label=\"log pdf\")\n",
    "l = l1 + l2\n",
    "labels = [l.get_label() for l in l]\n",
    "ax.set_title(r\"$Gam(a=10,b=1)$\", fontsize=15)\n",
    "plt.legend(l, labels, fontsize=12);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 424
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_logpdf = p.logpdf(xrange)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xrange, p_logpdf, label=\"pdf\")\n",
    "ax.scatter(z0, p.logpdf(z0), color=\"tab:gray\")\n",
    "\n",
    "ax.spines[\"right\"].set_visible(False)\n",
    "ax.spines[\"top\"].set_visible(False)\n",
    "\n",
    "lower_bound = p_logpdf[~np.isinf(p_logpdf)].min()\n",
    "upper_bound = p_logpdf.max() * 1.1\n",
    "\n",
    "for z in z0:\n",
    "    ax.vlines(z, lower_bound, p.logpdf(z), color=\"tab:gray\", linestyle=\"--\")\n",
    "ax.set_ylim(lower_bound, upper_bound)\n",
    "ax.set_ylabel(r\"$\\log \\ p({\\bf z})$\", fontsize=13,\n",
    "           rotation=0,\n",
    "           horizontalalignment=\"right\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "def finite_approx(f, x, eps=1e-5):\n",
    "    return (f(x + eps) - f(x - eps)) / (2 * eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  9.10271003,  -0.76087912, -14.22522469])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.sort(z0)\n",
    "lambda_n = finite_approx(p.logpdf, z)\n",
    "lambda_n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "m = (y1 - y0) / (x - x0)\n",
    "\n",
    "(x1 - x0) * m = (y1 - y0)\n",
    "\n",
    "y1 = (x1 - x0) * m + y0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_intersect(x1, x2, f, eps=1e-5):\n",
    "    \"\"\"\n",
    "    Compute the x-value that intersects two lines\n",
    "    of the form\n",
    "    yi = li * (x - xi) + f(zi)\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x1, x2: float\n",
    "        The tangent points\n",
    "    f: function\n",
    "        the target function\n",
    "    \"\"\"\n",
    "    l1 = finite_approx(f, x1, eps=eps)\n",
    "    l2 = finite_approx(f, x2, eps=eps)\n",
    "    den = (l1 - l2)\n",
    "    num = f(x2) - f(x1) + l1 * x1 - l2 * x2\n",
    "    return num / den\n",
    "\n",
    "\n",
    "def tangent_line(zi, z1, f, eps=1e-5):\n",
    "    return finite_approx(f, z1, eps=eps) * (zi - z1) + f(z1)\n",
    "\n",
    "\n",
    "def f_approx_gen(z, f, eps=1e-5):\n",
    "    \"\"\"\n",
    "    Parameters\n",
    "    ----------\n",
    "    z: np.array\n",
    "        evaluation points\n",
    "    slopes: np.array\n",
    "        slopes of approximating lines\n",
    "    f: function\n",
    "    \"\"\"\n",
    "    z = np.sort(z)\n",
    "    slopes = finite_approx(f, z, eps=eps)\n",
    "    @np.vectorize\n",
    "    def f_approx(zi):\n",
    "        if zi <= z.min():\n",
    "            return tangent_line(zi, z[0], f, eps)\n",
    "        elif zi >= z.max():\n",
    "            return tangent_line(zi, z[-1], f, eps)\n",
    "        else:\n",
    "            # find intermediate points\n",
    "            z1 = z[zi >= z].max()\n",
    "            z2 = z[zi <= z].min()\n",
    "            \n",
    "            intersect = compute_intersect(z1, z2, f)\n",
    "\n",
    "            if zi < intersect:\n",
    "                return tangent_line(zi, z1, f, eps)\n",
    "            else:\n",
    "                return tangent_line(zi, z2, f, eps)\n",
    "    \n",
    "    return f_approx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "zrange = np.linspace(0, 1, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 252,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "intersections = [compute_intersect(z1, z2, p.logpdf) for z1, z2 in zip(z[:-1], z[1:])]\n",
    "\n",
    "plt.plot(xrange, p_logpdf, label=\"pdf\")\n",
    "plt.scatter(z0, p.logpdf(z0), color=\"tab:gray\")\n",
    "\n",
    "for zi, li in zip(z, lambda_n):\n",
    "    y1 = (zrange - zi) * li + p.logpdf(zi)\n",
    "    plt.plot(zrange, y1, c=\"tab:orange\")\n",
    "    \n",
    "for x_intersect in [0] + intersections + [1]:\n",
    "    plt.axvline(x=x_intersect, c=\"tab:gray\", linestyle=\"dotted\")\n",
    "plt.ylim(lower_bound, 2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our first log-approximation is given by\n",
    "\n",
    "$$\n",
    "    \\log\\tilde q(z) = \\log p(z_n) + \\lambda_n (z - z_n)\n",
    "$$\n",
    "\n",
    "\n",
    "With\n",
    "$$\n",
    "    \\lambda_n = \\frac{d}{dz}\\log p(z)\\big\\vert_{z=z_n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fc9acb57c10>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_approx = f_approx_gen(z, p.logpdf)\n",
    "plt.plot(xrange, p_logpdf, label=\"pdf\")\n",
    "plt.plot(xrange, f_approx(xrange), linewidth=2)\n",
    "plt.scatter(z0, p.logpdf(z0), color=\"tab:gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With non-normalized probabilistic approximation given by\n",
    "\n",
    "$$\n",
    "    \\tilde q(z) = p(z_n)\\exp\\big(\\lambda_n (z - z_n)\\big)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fc9ad1a99d0>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_f_approx = f_approx_gen(z, p.logpdf)\n",
    "def f_approx(x): return np.exp(log_f_approx(x))\n",
    "plt.plot(xrange, p.pdf(xrange), label=\"pdf\")\n",
    "plt.plot(xrange, f_approx(xrange), linewidth=2)\n",
    "plt.scatter(z0, p.pdf(z0), color=\"tab:gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The normalization coefficient $Z_q$ is given by\n",
    "\n",
    "$$\n",
    "    Z_q = \\sum_{n=1}^{N_0}p(z_n)\\int_{i_{n-1}}^{i^{n}} \\exp\\big(\\lambda_n (z - z_n)\\big) dz\n",
    "$$\n",
    "\n",
    "where\n",
    "* $i_{n-1}$ is the lower bound for the part-function defined over the $n$-th observation: either an intersection point or lower bound of the domain.\n",
    "* $i_n$ is the upper bound for the part-function defined over the $n$-th observation: either an intersection point or the upper bound of the domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.23852225944672836, 2.6481290432337306e-15)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quad(f_approx, 0, intersections[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23852225944672847"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1 = lambda_n[0]\n",
    "(f_approx(intersections[0]) - f_approx(0)) / l1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9048232703888462, 1.0045556280023307e-14)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quad(f_approx, intersections[0], intersections[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9048232703888461"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1 = lambda_n[1]\n",
    "(f_approx(intersections[1]) - f_approx(intersections[0])) / l1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_norm, err = quad(f_approx, 0, 1)\n",
    "def q_dist(x): return f_approx(x) / Z_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WKUiNmfuY/+79MAIZXeKU/yT+GWOex94ed68dr4lttz8C2CV2zoRc7Vudd6PmkRXQ/4Xt8/E4tn3s38l6H113gAK5jgd6bhX0HHSX12Oep34z+VCQfSvr9n9RnUtFev4aY45i7/4MIeuOTDi2n8Vj2I6SSSLyiuSYWyMICuOHQqidf8Hi/v0UyHse6Hebq+28KsG0pl6FNGNMioi8ig1sYoH/Ax4MYFVXp9IIEYkKoBmA+wU92WuqECUil2LHqgZYA1xtvAxfJiKdi7Bcgm1X7WpKMMYY87af1dy/hGr7qtXOQz6BTCpU1n+SwBhjpgHTnD9Cu2KHg+sGtMTWCl4HXCIinYwxm9xWHURWO+r/Af2dzWNyEZEXglXeQpLXY37Sa6ri5x48FdW5VOTnr7Ovxosi8n/Y2vrOQBdsx+Eq2KDwJaCjiFzn565OcSvK868oK0jdv58Cec9L9HebyhutqVclwSjsWN0A94tIfV+Jnfa5/R9IMwZXGoMdK7mkcZ9t9gVvAb3ThT5eC7bB2BpqsO1mBwawjvut+IJ0NnXveBfIORNImjwxxuw1xnxljHncGNMKOyzkPOfLcWSN6+3ieh/TgSe8BfRORfk+5kdej3mwO0oGk3vZ6gaQPpA0edlmkZ6/zpGyVhljhhtjegIJ2LtDrn4p3bFzDISyvBwzT9d99zu8/u5MFOWAA/n9boPQ/oypINCgXoU8Y0watoYe7N2lV3wkd3HvdJpzspRsRKQmdgxqsGPlB3NYtaKS4Pb/Dm+JnLfNuxV6aey2epL1vu0C/h7AHROwky655HtUCmcHMlctf+sAOlp7GsYwqJwjmNxO1qgbXXIkcb2Ph30Na+nsdFzV2+shoksAzTQud/t/WWEWpiCcHbp3Ox+2CaBTZbcgbNb9GnaFr4TOPitNfKUpCGeQP52szzPkPnfdm25IYZUlD/wds+pkHbOtHjo/u3/+vDb7FJFw7KRcvgTt2Hi4rvm7Drj3sQr2UKQqxGhQr0qKCdgZAcGOA93KT/qv3f5/1M8QkE+T9VmYmr/iFTv39qP1fKR7iCIIBkWkI1nDGZ4A/mYCn4FwDlkdtu4RkYLU1k9z/o3CxxwEzplU89LBON+cwcNR58OcTSBd72M1EfHV/vX/fLwWKuKBvt5eFJFryLoT86tzNJJQNsP5NxofTQCdfSWuC8L2lpDVtv0mEfH1uX6CIugfg53zwyXnuevefCVoTdkK4FoR8fVD5zGyjtnXHl53H03I1w+Envi/pgb72Li+pyLwMdyz8xrysPOhayI/VYppUK9KBGfbTVcbYiFrUhZv6deSNVZ0XWC0p1pDEbmbrGAvmawxfUsa91rO/xORXKMTiMiN2BEuCpXzzscM7AgiGdjJugIebs85udK/nQ+jgDki4rMmTEQ6iIinkXKGk3Ub/QVnIJlz3QTslOgFDopE5DERuU1EIn2k6UHW7fqccx643kchazx/93VFRF7B/3jToeK/IpJrqEpngPq521Nex9oOIcPJGs//ZRG5PGcC592gCWRNUpVvzjuUrrkVooBJnu42OYd1/UdBtycinzp/3Hp7PQIY4PZUznPXfeK7tgUtTxBEAF95qsl2XgtdE56dJmsCQndzybqj9oiI5Gru5rwueZ3/wk2wj80HZHUufkZEbvNQthjsHB6uuwxT/cx1oEoB7SirSgxjzCwR+QXb6TCQ2o4HsFO2V8XWprQVkf9hhzGrCNxE9nahDznHey6JpmHbop+PHaN/o4iMwg6tVxG4HrgR+wX2Nf4n2SqI4djh4QC+A6KdgYcvK53zBQBgjBnuDAbvwY41v1REvsOOPb0bG/RWAVpgm83UwzY7yjbkqTFmh4i8hB0aMxr4VkS+wn5hp2I7rvZ35jWNgk9C0xY7gctREfkBWIF9XxzYY3INWbMxGuD1HOt/CNyH/YHxmIi0xr5f+7Ej6NwFtMHWIqZgRyYJVXOwTd+WOD93i7BBUgfsbLKuDnxfO2dFDWnGmM0iMgTbTyQWmCsiE7Bj7adih0a8H9uEajLQw7lqQUYUeRvbXKs19tzaKCKfYUc+KoudNfs27FCMqylYs58BwAAR2YAdvnI9tg19WWzFSE+y2mdvxY62lckYc1REVmHPz8tF5GPs5zXZLc13BShfXk3H/vjd4Dxm67CdZ7tj3xtXM5h/GQ+zeBtj9orIl9jRw+KBZSLyIfazVw57rHth77r9hO/a/HXYWZ2rAX1E5CB2THhXYJ5ijPnZ28oeypYoIk9iJ0GLAKaIyAzsZ+4Y9n26j6y+HXvwP1u6Kg2MMbroUqwLNrgx2Pbs/tJe6pbetQz2kb4hdmKpnOu4L6eAe3zk0c8tbb8A9ynRmT7RT7pugeyHM+0Yt7S1Pbx+MfZL2Nt+HsUG94PdnuvmIZ/abq+PyWtZsBPv+DrenpZcxxX7pfsiNmAKJI8FPo7df7DBlbd1h+XlvfCxnc8DLOtJ4G4veTyEDX69rbsR28Ev8zh7ycfn+1wY52vO14E+ft6/2UBMANcGj++tv30kgHM5r2mxM5H6em/fw3Z4dj1+Mj/nktv2qmErJ3x9rq/C//XB33vn6/PhvqzxlL8zj+uwnbw9rpvf8zPQ8zRnntgKBm/74fB0HHLkFw+s8pHHXuyETj6PvTOvB3zkk5ifY4NtBpbi5/1a561MzjwWeHp/CppWl+JZtPmNKlGMMQuxtb+Bpt+Krc0dAHyPrfFMw34RrsQGew2MMWODX9qiZYz5DdvXYDi21vostgZvPXYCr1bGmDnFV8K8MdZrQB1sG/Kfse/fWWyguBs7ksyrQCdjTDcfeT2P/UE4GTt6xFls7dVM4HpjzGNBKvaD2GDiFWxt5x5s8590bD+BxcDLQENjzDgvZf0IO5TgZLLO1wPYyav+AbQ3dsr2kGeM+QJbMz8Se9coFfvD8yegtzHmBmNMajEWMc+MMU9ga2Wnkv1cmg5c63y9stsq/mYy9re9A9jA8VFs7e4J7B23LcBQoLUxZp73HAJWHVvz/Bn22ngU++MyBRtMTwN6A22NMYleyvot9tz9EtvkpDDGnw+YMWYQ9m7sN9gA/Kzz71dAZ2PMYD/rH8HeGX4WG9yfJGvW5SHYa6rX2Zpz5PUp9s7KdOy1K5D5U/zl+TG24upN7J2aY9h93Iettb8Xe34kFnRbqmQQY399KaWUUgUiIt2wP2YA/u0vaCqtROQdstq5tzXGrCrO8iilzg1aU6+UUkoFiXO4y7udDw9hmz8opVSh06BeKaWUCoCIVHcOWent9YrYZlOuEVc+N74nEFNKqaDR0W+UUkqpwNQHForI79h+AVuxbazjsKPT9AIqOdPuxMOwpEopVVg0qFdKKaUCJ9iRpi72kWYdcKMxJtlHGqWUCioN6pVSSqnALMfO8XAtdkSaqtiRbhzAQefrXwMTjTEZ3jJRSqnCoKPfKKWUUkopVcJpR1mllFJKKaVKOA3qlVJKKaWUKuE0qFdKKaWUUqqE06BeKaWUUkqpEk5Hv/FDRHYBFYDEYi6KUkoppZQq3WoDJ4wxdfK6ogb1/lWIjY2Nb9KkSXxxF0QppZRSSpVemzZtIiUlJV/ralDvX2KTJk3iV6xYUdzlUEoppZRSpVi7du1YuXJlYn7W1Tb1SimllFJKlXAa1CullFJKKVXCaVCvlFJKKaVUCadBvVJKKaWUUiWcBvVKKaWUUkqVcBrUK6WUUkopVcJpUK+UUkoppVQJp0G9UkoppZRSJZwG9UoppZRSSpVwOqNsIUlNTeXEiRMkJyeTlpaGMaa4i6SKiIgQGRlJ+fLlqVChAjExMcVdJKWUUkqVchrUF4KTJ0+ye/duDeTPUcYYzp49y+HDhzly5AgXXHAB5cqVK+5iKaWUUqoU06A+yFJTUzMD+goVKlCpUiViYmIIC9OWTucKh8NBamoqR48e5cSJE+zevZs6deoQHR1d3EVTSimlVCmlQX2QnThxIjOgr1GjBiJS3EVSRSwsLIwyZcoQGxsL2HPi+PHjVKtWrZhLppRSSqnSSquPgyw5ORmASpUqaUB/jhMRKlWqBGSdF0oppZRShUGD+iBLS0sD0M6RCsg6D1znhVJKKaVUYdCgPshcnWO1Db0CMu/WaKfpc8yhbfDbR/DHr6DvvVJKqSKgbeqVKkTaBOscdHgHfHgxONLt45oXw2XPQL0rQM8HpZRShUSrk5VSKphWjcsK6AH++g2++DuMvAq2/qA190oppQqFBvVKKRVM+9Z6fn7PcviyB3zaDTbP0eBeKaVUUGlQr5RSwbR/ne/X962Gib3g466wYTo4HEVTLqWUUqWaBvVKKRUsyUlw6kDW44gYaHid57RJ62ByX/ioE6ydDI6MoimjUkqpUkmDeqWUCpb9OZreVGsKd02EgQuh8d88r3NwM3zdH4Z3gFXjIUOHP1VKKZV3GtSrUqtLly5ERESwffv2AuXjcDho3Lgx5cqVIykpKUilU6VSzqD+vJbOv62g53h4cAk0uxXwMArOkR0w42H4oC0s/xzSzxR6cZVSSpUeOqSlKpVmzpzJkiVL6N27N/Xr1y9QXmFhYTz33HP069ePV199leHDhweplKrUydmevnqLHI+bQ48x0G0LLHoH1k0Gk6NN/bE/YdaT8PNb0PlxaNsXosoUarFVyWaM4djpNP46epq/jqSw++hp9p9I5fSZDE6nZZByNp3TZzM4fTaD1LQMoiPDKRMZTpmocGKj7N8yURFUj4uhVnwZasWXoWZ8GeJiI4t715RSeSA6KY5vIrKibdu2bVesWBFQ+k2bNgHQpEmTwiyW8sHhcNCyZUs2btzIhg0bgvJepKen07BhQ3bv3s2WLVuoU6dOwOvqOXEOGdbW1ri73D8Xanb0nv7wDlj0LqydmH0YTHdlqsAlg6D9/RBTIbjlVSVOytkMNuw9zuq/jrFm93G2JSWz+2gKJ894OX8KIC42klrxZWiQUI52F1ai3YWVaFCtPOFhOt+CUoWlXbt2rFy5cqUxpl1e1w1KTb2I3A5cBrQGWgHlgfHGmD55yKMfMNpPMocxJtxtndrALh/pvzLG9Ay0DKp0+P7779mwYQNdu3YNWiAdERFB3759GTx4MMOHD+edd94JSr6qFDmTDEd2uj0hkNDM9zqV68EtI+zkVEveg1VfQMbZ7GlOH4J5g2HxULjoQbuUiQ926VWIOpCcysKth1jxxxFW/3WcrUnJZDiKpjLueEoa6/YcZ92e43y9cg8A5aIjaFOrIm1qVeKiOvF0rBNPZLi25FUqFASr+c2L2GD+JLAbaJyPPFYD//byWlfgCuBbL6+vAaZ7eH59PsqhSriRI0cC0LNncH/P9erVi8GDBzNu3DjeeOMNIiP11rRyk7QRcAu2KteHqLKBrVvpQvjbULj0afjlA1g+GtJTsqdJPQ4/vwm/DIcO90OnQVA+IWjFV6Ehw2FY/dcxFmw5wPwtB1i/50RA65WJCqdmpTLUjI/lgkplqFExhnLRkbma2ERHhHEm3UHK2QxOn00nJc02yzl1Jp09x1L468hp/nQuqWm5h1s9eSadRdsOsWjbIcDW5l/VJIFrm1ena4MqxESG51pHKVU0ghXUP4kN5rdja+zn5zUDY8xqbGCfi4j86vz3Uy+rrzbGDM7rNlXo6tOnD+PHj+eFF17g3nvv5a233uLHH39kz549REdH07VrV15//XWaN2+ebb3Dhw/zzTffICL06NHDY96zZs3ixhtv9FuGSpUqceTIkczHDRs2pFWrVqxZs4ZZs2Zx6623FmwnVemSs5Nszvb0gahQA659Hbr8A34bAUtHwtnk7GnSTsEvw2Dpp9Dmbuj8GFSslf9yq2KXnuFg0fZDzFy9l/lbDnDstPcRkESgXtVytLqgIq1rxtHs/DhqVy5LpTKRiASvWYwxhoMnz5B46DRr/jrGyj+PsvyPoxxMzt6B+3hKGlNX7mbqyt2UiQrn8kbVuLZ5da5plkB0hAb4ShWloAT1xpjMID6YFxVnfs2Bi4E9wOygZq5C1urV9vfd4cOHad68OampqcTExOBwODh+/DizZs1i4cKFLF26lEaNGmWuN3/+fNLS0mjYsCFVq1b1mHdiYiIJCd5rOA8dOkRGRgatWrXK9Vrnzp1Zs2YNP65KyFAAACAASURBVPzwgwb1KjtvI9/kR7mqcNVg21H290/gt48g9Vj2NOmpsOwzWDEaWt4JnZ+Aqg3zv01VpIwxbNx3gq9X7mHG6r0cOul5tKOIMKF97Up0bVCVNrUq0uL8OMrHFP5dQhGhWvkYqpWPoWOd+Mwy7z6awso/j7Is8Qg/bjrAvuOpmeucPpvB7HX7mL1uH/Flo7izQ016X1SLCyppR2+likJJGP1moPPvKGOMt9lZaojIQKAycBj41RjjZa52FerOnDnDli1bAPj4449p1KgRw4YN4+qrryY9PZ0pU6YwYMAATpw4wQsvvMCUKVMy112yZAlgO5p4M2jQIAYNGuTxtVGjRjFgwABiY2N56aWXcr3evn17ABYtWpTv/VOllL+Rb/IjthJ0exY6PWKHufxlePbJrcB2sF09HlZ/CU1vsrX8NVoXfNuqUBw5dZbJy//i65V72JKU7DFNtfLRXN6oGt0aVaVzgypUKIIgPhAiQk3nyDg3tz6fV282rN19nO837Oe79fvZeehUZtojp87y0YIdfPLzDq5onMA9nS6kS/0qhGknW6UKTUgH9SISC/QBHMBIH0mvdi7u6y4A+hpj/gxwW96Gt8lP/wBVAOvXryc93Y7k0KRJE5YsWUKlSpUAiIyMpFevXmzevJlXXnmFb7/9loyMDMLD7W3epUuXAtCyZd5rSUePHs2AAQOIjo5mxowZXHHFFbnSuGrvN27cSHJyMuXLl8/XPqpSJiPN2abeTfUC1NTnFF3e1tp3fABWjoMl78OJ3TkSGdg4wy71r4Ku/4QLLwleGVSBbE1KZvSSXXy9cg9n0nO3Va9aPppbWtfg5tbn06xGhaDf9S4MIkKrmhVpVbMiT3dvxPYDJ5m9bh+Tlv3FXmcNvsPAvE1JzNuURN0qZXmwWz3+3uZ8IrRzrVJBF9JBPXAHUBGYbYz5y8Prp4FXsZ1kXcNOtAQGA5cDP4pIa2PMKQ/rFqvaz5aelkSJb9wQ1PzWrFmT+f+oUaMyA3p3119/Pa+88gqnT58mKSmJGjVqALBv3z4AqlSpkqdtjh07lv79+xMVFcX06dO5+uqrPaZz5WuMISkpSYN6ZR3aBhluzSfKVYdy1YK/nchYuOgBaNcP1n5lR8w57GFyte3z7FLzYhvcN7jaNsZWRcrhMPy87SCfL96V2bHUXUxkGNc2q86tbS+gc73KJTrQFREaJJTniYTyDLq8Pj9uPsC4X/9g8fas/d556BTPTFnLxwt28MTVDflbi/O05l6pIAr1oP4B599PPL1ojDkA/F+OpxeKyDXAYuAioD/wvr8NeRsP1FmD3zbQAquCc7Wn79y5M506dfKY5rzzzsv8371G69Ah+wXi6YeAN+PHj+fee+8lIiKCqVOn0r17d69p3fM9dOhQgSe2UqVEYTS98SUiCtreDa3vsjXzi96FpHW50/31G3zZAxJaQJcn7Gy2Ydp5sbClZziYvnovHy3Yzo6DueuUmp9fgXs61eb6FudRLjrUv4bzLiI8jO7NqtO9WXV2HDzJF7/9wZQVu0lOtXdgdx46xWMTVvHh/O08eXVDrmmaUCLuTCgV6kL2aiIiTYFLsKPqzMnLusaYdBEZiQ3qLyWAoF6FDldQ76sjqmtUGhHJ1iH2zBlbWxoVFRXQtiZOnEjfvn0JDw9nypQp3HCD77sOMTExmf+npKT4SKnOKcEY+SY/wsKh+d9tsL5tLiz6L/z1e+50Setg6v3w02u2GU/ruyAiumjKeA7JcBhmrd3L+/O2ZWtfDhAmcE3T6tzXpQ4dalc6Z4LYelXL8fKNzfjnNY0YvXgXny7amRncb96fzMBxK2h5QRzPX9+Ei+tWLubSKlWyhWxQT2AdZH056Pwb4EDRRSvYTVZKk7VrbYDUtq33GyTLly8HoFmzZkREZJ3G8fHx7N+/n2PHjnlbNdOkSZPo06cPYWFhTJo0KaBhLo8ePZr5f+XK+gWknII58k1+iEDDa2wzmz+W2Jr7HT/mTnd0F8x6Aha8YTvftr/XttdXBeJwGL5dv5/35m1l24GT2V4rFx3BnR1q0u+S2tSMP3dHgSkXHcGjVzbgnk61+XTRDkYvSeT0WfvVvnb3cXp++hu3t7uA569vQnzZwCpllFLZhWRQLyIxwN3YDrKj8pnNxc6/O32mUiFl165dHD9+HPAdNE+dOhWwbevdValShf3792cLvr2t37t3b0SECRMmcMsttwRUPvd889puX5VSxnhoflPEQb2LCNTuYpe9q+0stBtnkG1SLICT+2HuS7Zmv8MAuPghKKvnc14ZY5i/5QBvfbeFzfuzj2RTISaCAV3r0q9z7SIZgrKkiCsTydPdG3Nv5zp8tGAH4377g7POjsNTVuxm3qYknr+uCT3aX3DO3M1QKliKvFeOiESKSGMRqecjWQ+gEjDHSwdZV14XiUiun/QicgV2QiyALwpUYFWk3DvJutrH57Ru3Tp++OEHIiIieOCBB7K95hqzfteuXV63MX36dHr16oUxhvHjx3PbbbcFXL7ExEQA4uLiqF69esDrqVLs+G5IcfsRGVUOKtUpvvK41GgNd/wPBi2DNn0gzENgmXrcBvZDm8Ocp+HoH0VfzhJq+4Fk+o1exn1jlmcL6MtFR/DYlQ1Y9K8rePTKBhrQe1GlXDQv/a0pC57qxnXNs66lx06n8czUtdz5yW9s8zLkp1LKs6AE9SJyi4iMEZExwLPOpzu5nhOR/7olPx/YBHi4N5zJFal5m0HW5U1gj4hMFpGhzuVHZ97RwEvGmF/yvEOq2Lja0wP88MMPuV5PSUnh/vvvx+FwcN9991GvXvbfhp07dwaymufkNHPmTO644w4cDgfjxo3jjjvuyFP5li1blrmdsLCSO1KFCqKctfQJzSGUzo0qDeDmEfD4Grj4EYj00AQkPcXOUDusDUwdAPvXF305S4jjp9N45ZuNXPveIn7eejDz+TJR4TzcrR6Lnrmcf1zdkLhYDeYDUaNiLB/1acfn/dpzfsXYzOeXJh7h+mGLGDp3K+kZuYcAVUrlFqzmN62Bvjmeq+tcAP4AngokIxFpAnQhsA6y44BbgQ7AdUAkkARMAoYbY3SGoBLGVVMfFxfHsGHDaN68OXfeeSeRkZH8+uuvPPHEEyxbtowmTZrw7rvv5lq/S5cuAKxatSrb+PUAs2fPpkePHmRkZPC///2PXr165bl8rqC+a9eu+dk9VRoVVyfZvIo7H679D1z6lA3gf/84+x0GAJMB6ybZpf7V0OVJO9a9NoMgw2GYuOxP3vlhK0dOnc18PkygZ8da/OPqhlQpp52P8+uKxglc/I/KvP/jNkYt2kW6w5CWYXj/x20s3n6I93u21plplfJDjDH+U53DRGRF27Zt265Y4W1uquw2bdoE2EmTVN7VqVOHxMRExowZw1NPPcWhQ4eIjIwkIiIic7SZxo0b891333HhhRfmWt8YQ/369dm5cyfz5s3jyiuvzHytffv2rFixgoiICJ/t9Rs2bMjChQtzPZ+amkq1atU4efIk27Zty3WXwBs9J0q5ib1h86ysxzcOg3Y56zhC0NlTsOJ/8OtwOLHHe7oLOtgRcxrdEFp3IIrQ+j3H+dfUtWzYeyLb8xfVieflG5vRtEaFYipZ6bR5/wlemLaeFX9k/egsHxPBG39vyQ0tz/OxplIlX7t27Vi5cuVKb0Ot+3JuXqFVSDp+/Hhmm/Vrr72WJUuWcNtttxEXF4cxhhYtWjBkyBBWrlzpMaAHO8TlfffdB9jhKl3S09PZsGFD5v9JSUlel4SEBI95z5o1i+TkZLp16xZwQK/OAcU98k1+RZWFTg/DY6vh5g+hSiPP6XYvg6/6wIiOsHIspJ/xnK4USk3L4PVvN3HziCXZAvrzK8byUe+2THzgYg3oC0Hj6hWYNLATT3dvRLhzcqrk1HQe+XIlz05dy+mz6cVcQqVCk9bU+6E19UVn4cKFXHbZZSQkJLB///5857N3715q165N+fLl2bt3L9HRwbklftttt/H111/z5Zdf5qnpjp4TpVjKUXizdtZjCYfn90JkjNdVQpbDAVu/hcXvwe6l3tOVq25Hy2l/L8TEFV35itivOw7z3NdrSTx8OvO56IgwBl1enwGX1iUmUifxKgor/zzKYxNWsfto1rwg9aqW5YNebfUHlSqVtKZelQquTrItWxasprNGjRoMHDiQI0eOMHr06GAUje3btzNjxgyaNm3KnXfeGZQ8VSmQs0Np1UYlM6AH27Sm8Q1w/w9w77fQ4BrP6U7uh3kv2xFzfngJTuwt2nIWsuMpaTw7dS29PvstW0DfqW5lvn/iUh69soEG9EWoba1KzHm8Kze2qpH53I6Dp7j1wyV8s6Z0nXtKFZQG9SpkuDrJtmrVqsB5vfTSS5QrV44333yT9PSC36p9/fXXycjIYMiQITrqjcoSKuPTB5OI7RzbezI89Au07AlhHsZUOHMCfhkG77WE6Y/Agc1FX9YgW7ztENcM/ZmJy7JGUrZtuVvw5YCLqF0lJOcyLPUqxEQyrGdr3r69JWWi7A+qM+kOHp2winfnbsXh0BYHSoEG9SqEBKumHqBatWqMHTuWvn37snv37gLl5XA4qFevHm+//XbAk1Spc0RJGfkmvxKawd8/se3uL34YIj0EtY40WP0FfHgRfHknJC6xE3KVIKlpGbw6ayN9Rv1O0omsPgPdmyUw7x+X0bNjLZ0IqZiJCD3a1+SbR7tQt2rWeTjsx20MmrCSlLP5mXheqdJF29T7oW3qi0Z6ejrlypXjzJkzrF69Oii19aFCz4lS7KPOkOTWBOeemVD3suIrT2E7fQSWjbLDYZ72PDkcAOe3g0segyY3QlhoN1XZsj+ZxyeuyjaBVOWyUbx6S3Oub6EjrYSi4ylpDPpyJYu2ZZ2DLc6P47N72lM9roQ2f1PKSdvUqxIvIiKC1NRUjDGlKqBXpVj6GTiYo8lJaaupz6lMPFz2NDy5Hm54F+Lrek63ZwVM7gsftIWln9nhM0OMw2H4fPEubhy+OFtAf3mjqnz3xKUa0IewuNhIRvfrQL9Lamc+t27PcW4avpg1fx0rvoIpVcw0qFdKqfw4sAkcbv014mraoPdcEBkLHe6HQcvhjrG2Zt6To4kw5ykY2gx+GgInDxRpMb05dPIM/cYs45VZGzmbbmcrjY4I45Wbm/F5vw5ULa+TSIW6iPAwBt/UjNduaZ457OWB5DPc8cmvzN8cGueZUkVNg3qllMqPXJ1kS3ktvSdh4dD0Zuj/I/SbAw26e06XchQWvmVHzJn5GBzcWrTldLM88Qh/G7aYhVsPZj7X9LwKzHq0C/d0qq1t50uYPhdfyLj7OhIXGwnYDrQDxi5n1lodGUedezSoV0qp/MjVSbYUjHyTXyJQuzP0ngQP/w5t+kB4VO50GWdg5f9gRAf4smeRdqo1xjBy0U56fvob+0+kZhZ74KV1mfbIJTRIKF8k5VDBd0n9Kkx/pDMXVIoFIN1heGzCKia5jWKk1LlAg3qllMqPfaV85Jv8qtYYbh4BT6yDLv/wPkHV1m9hzPXw2RWwfipkFN4socmpaTw8fiWvzd5EunP4w4plbLvs565vQnREaHfmVf7VqVKWKQ9eQj3nyDgOA89MXcuoxbuKuWRKFR0N6pVSKq8cjtzNb847h2vqPSlfHa56GZ7cAN1fh7hantPtXQlT7oNhbeDXEZB6IqjF2LTvBDcNX8K367NmqW5VsyKzH+tKt0bVgrotVbyqx8UwaWAnmrnNNPvqrI0M+3EbOtKfOhdoUK+UUnl1ZAekuY3oElvJdpRVuUWXh04Pw2Or4PbPoUYbz+mO/wnfP2871f7wIhwv2PwSADNW7+HWD5ew61DWe3VPpwuZNPBizq8YW+D8VeipXC6aLwdcTPsLK2U+9+7crfxnziYN7FWpp0G9Ukrl1b412R9Xb2kbaCvvwiOg+W0wYL7tVNvwOs/pzpyAXz6A91vB1P6wZ2WeN+VwGN7+fjOPT1xNapod3aZMVDjv92zNKzc31+Y2pVxcbCRj7+9I1wZVMp/7bNEuhszWwF6VbhrUK6VUXuXsJHuezq0QMFen2rsmwiPLoF0/iPAwYZAjHdZNhs8uh9HXw+bZ4PA/a+jJM+kM/GIFI+bvyHyubtWyzBzUmZtbnx/EHVGhrExUBCP7tqd7s4TM50Yu3sWwH7cXY6mUKlwa1CulVF7lrKnXoD5/qjaEG9+37e67PQdlqnhO98cSmHgXDG8Pv38KZ056TPbXkdPc/tEvzN2YlPncZQ2rMu3hztSvpqPbnGuiI8IZcVdbrm1WPfO5ofO2MnLRzmIslVKFR4N6pZTKC2M8jHyjnWQLpGwV6Pasnan2xvehSkPP6Y7shG+fhqFNYe7/ZWt3//vOw9w8Ykm22WH7d6nD5/06ZI5hrs49EeFhvN+rNZc2rJr53GuzNzFx6Z/FWCqlCocG9UoplRcn9kDKkazHkWWhcr3iK09pEhlrm+M8/DvcNRnqXOY5XepxWPI+vNcSptzHvLlz6DPqd46cOmuzCRfeur0lL/6taeZso+rcFR0Rzid92tGxdtaMz89NW8c3a3SCKlW6aFCvlFJ5kauTbHM7s6oKnrAwaHgN9J0JDy6GVndBmIfadpMB66dy1ZJeTAh/mevCfiehbDgTBlzMHe11NCKVJTYqnJH92tPifDtvgjHw5Fer+XFTkp81lSo5NKhXSqm8yNn0RtvTF67qLeDWj2zTnK5PQWy8x2Ttw7byUdT7LCnzT9rvHW9r85VyUyEmkv/d15EG1coBdubZh8av5Ledh4u5ZEoFhwb1SimVF56Gs1SFr3x1uPIleHIDqde+y94IzzXxEcm77Tj37zaFOc/A4R0e06lzU3zZKL7ofxG14ssAcDbdwcBxK9hx0HPna6VKEg3qlVIqL3INZ6lBfVE6kBrGbUsb0vnk6/Q7+wwLM1p4Tnj2JCz9BD5oBxN6wc6fbZsLdc5LqBDD+P4XUa18NADHU9K4b8yyzD4ZSpVUGtSrUqtLly5ERESwfXvBxiV2OBw0btyYcuXKkZSk7S/PaacO2Y6yLmGRULVJ8ZXnHLP9wElu/fAXNuw9gSGMBY7WLO86CvPgEmhzN4RHe1jLwJY5MPYm+KgzrBwLaSlFXnYVWmrGl2FU3w7ERtr+MH8cPs3Accs5k+5/LgSlQpUG9apUmjlzJkuWLKFnz57Ur1+/QHmFhYXx3HPPcerUKV599dUglVCVSDmb3lRrAhFRxVOWc8za3cfo8fEv7DlmA/LwMOH1v7fgH9c0Qqo3h5uHwz82wuUvQLkEz5kc2AAzH4WhzeDHV+HEviLcAxVqWlwQx3s9W2dOBr0s8SjPTl2ns86qEkuDelXqOBwOnn/+eUSEF154ISh59u7dmzp16vDpp5+ya9euoOSpSiCdSbZY/LrjMHd99jtHT6cBEBsZzsh72tOrY63sCctWgcuegSfWwa2feO/vcPowLPovvNccpvaH3csLeQ9UqOrerDrPXdc48/G0VXt01llVYmlQr0qd77//ng0bNtClSxeaNAlO04iIiAj69u1LWloaw4cPD0qeqgTSmWSL3LyNSfQdvZSTZ9IBqFgmkgkPXMzljat5XykiGlr1hIELod8caHIjiIevO0c6rJsMI6+Ez66EtZMhXdtVn2sGdK1Lr45ZHa+HztvKjNV7fKyhVGjSoF6VOiNHjgSgZ8+eQc23V69eAIwbN460tLSg5q1KCJ1JtkhNX7WHgV+s4Gy6A4Bq5aOZNLATrWtWDCwDEajdGe78Ah5bDZc8CtFxntPuWQ5f94f3WsDPb8HJg0HaCxXqRIRXbm5Ol/pVMp97evJalice8bGWUqFHg3oVsowxfPnll3Tr1o2KFStSoUIFLrnkEmbOnAlA9erVERGWLFmSuc7hw4f55ptvEBF69OjhMd9Zs2YhIn6X+Pjs42E3bNiQVq1acfDgQWbNmlV4O65CU+oJOOI+PKLYiadUoRj3ayJPTlpNhsO2b64VX4YpD15Cw4Ty+cuw0oVwzWu23f31/4XKDTynO7kf5g+BoU1h2oOwd1X+tqdKlMjwMEb0bkt95xj2ZzMcPDR+JQdOpBZzyZQKnAb1KiSlpKRw880307t3b37++WdOnTpFRkYGv/76K7fccgvjxo0jKSkJEaFFi6wh7ebPn09aWhoNGjSgatWqHvNOTEwkISHB6xIebkdDaNUqd9OKzp07A/DDDz8Uwl6rkJa0PvvjKg0gqmzxlKWUGzF/Oy/N2JA5AmWjhPJMebATtSqXKXjm0eWg4wB4ZCn0ngr1r/acLuMsrJkAn3aDUdfAuimQoXfoSrO42EhG9+tAfFnb+f1g8hkGfbmKtAxHMZdMqcBoUK9C0oABA/jmm2+oUaMGkyZNIiUlheTkZBYtWsQFF1zAoEGDAKhTpw4VKlTIXM9Va9+uXTuveQ8aNIj9+/d7XIYMGYLD4SA2NpaXXnop17rt27cHYNGiRcHcXVUS6Eyyhc4Yw9C5W3n7+y2Zz7WuWZGvBl5MtQoxwd1YWBg0uAr6TIFBy6HDAIj08iPtr99h6v1uTXMOBLcsKmTUjC/DsJ5tCHOOiLM08Ui281GpUBZR3AU4Jw320qazpBoc3OnYx48fz/jx46lSpQqLFy+mTp06ma916dKFESNGcNNNNwG5a9OXLl0KQMuWeW/rPHr0aAYMGEB0dDQzZszgiiuuyJXGtb2NGzeSnJxM+fL5bAqgSh6dSbZQGWN4d+5WPvgpa+SRS+pV5rN72lM2upC/qqo0gBv+a2esXfUFLP0UjibmTpe8zzbNWfg2NLsVOg6EC7xXIKiSqUuDKvzzmkaZwfynC3fStlZFrm1+XjGXTCnftKZehZT09HRefvllAN58881sAb1L9+7dEefAwjmD+n377LjTVapUybWeL2PHjqV///5ERUUxffp0rr7a8y15V77GGJ2I6lyjM8kWGmMMb32/JVtAf1nDqnzer0PhB/TuYuKg0yPw6Ero9RXUvdxzuoyzsPYrGHkFfHYFrJkI6WeKrpyq0D10WT2udBth6anJa9l58GQxlkgp/zSoVyHlu+++Y8eOHVStWpW7777bY5qoqCgqVaoE5A7qDx06BJD5eiDGjx/PvffeS0REBFOnTqV79+5e07rn69qWOgekpcLBzdmf05r6oDDG8J85m/hoQVYn5CsaV+OTu9sR45zts8iFhUOja+Ge6bbtfYf+3pvm7FkB0wbaCa1+eg2O61CIpUFYmPDuHa2pGR8LwMkz6Tz0xUpOn00v5pIp5Z0G9SqkfPvttwDccMMNREZGekxjjOHEiRNA7qD+zBlbWxYVFdgsnxMnTqRv376Eh4czZcoUbrjhBp/pY2Ky2vWmpOhU8+eMAxvtmOYucbWgTLz39CogxhhembWRzxZlTeh2VZMEPurTtvgC+pyqNoIb3rGj5nR/HSrlvnsIwKmDtlnOey1g0j2QuBh0ZtISLa5MJB/1bkd0hA2VtiQl88K09TrjrApZ2qa+OAS5DXppsmaNbbfcpk0br2k2bdpEeno6FSpUyNU8Jz4+nv3793Ps2DG/25o0aRJ9+vQhLCyMSZMmceONN/pd5+jRo5n/V65c2W96VUpo05ugM8YweOYG/vfrH5nPdW+WwAe92hIVEYL1TbEVodPDcNGDsH0eLP3E/s3JZMDGGXap1tTW8re80466o0qc5ufH8eotzXlmir0GTFu1h7a1KnJ3p9rFWzClPAjBK6c6l7naqftqPjNt2jTA85CTrjbv7sG3J1OnTqV3796ICBMmTOCWW24JqHzu+ea13b4qwXQm2aAyxvDqrE3ZAvrrW1Rn+F0hGtC7CwuDhtdAn6kwaIUN8qMreE57YCPM/ge82wS+/Rcc2la0ZVVBcUf7mvTskDXj7KuzN7F5/4liLJFSnoX41VOdq7x1Qj1+/DjDhw8HPAf1jRo1AmDXrl25XnOZPn06vXr1whjD+PHjue222wIuV2JiIgBxcXFUr1494PVUCaczyQaNq1Ps50uyPqN/a3kew3q2ITK8hH0lVakP171pm+bc8A5UbeI53ZkT8PvHMLw9jL0FNs8GR0bRllUVyOCbmtGshv3xdjbdweMTVpOapu+hCi0l7AqqSrv69esDnid3cjgc9O/fn/379wO+J4davny5x/xnzpzJHXfcgcPhYNy4cdxxxx15Kt+yZcsytxMWph+fc0JGOiRtyP6c1tTn2/s/bsvWKfa65tV5787WRJS0gN5ddHnbzObhX6HvLGhyE4iXPgE758PEu+D9VrDoHTh5sGjLqvIlJjKc93u2ISYyq339W9/p+PUqtJTgq6gqjVzjz8+dO5chQ4Zw+vRpANavX88NN9zA3LlzM9N6Cuq7dOkCwKpVq8jIyF6LMnv2bHr06EFGRgZjxoyhV69eeS6fK6jv2rVrntdVJdThbZDu1im6bFUor3dp8uPDBdt5b15WE5SrmlTj/Z5tSnZA704E6nSFO8fBE2uh61P2fPHk+F/w4yswtClMHQB//q4da0Nc/WrleOGGppmPP1+yi4Vb9UeZCh2l5EqqSov7778/s5Psiy++SPny5SlfvjwtWrRg2bJlDB06FIDw8HCaN2+ea/327dtTt25dTp06xYIFC7K99vLLL3P27FnCwsJ46qmnqF69usfl0ksv9Vi21NRU5s+fj4jQo0eP4O64Cl2emt4450lQgRu5aGe2ms1LG1ZlRO8S0IY+v+IusJNZPbkB/v4ZXNDRc7qMs7BuEnx+DXzSFVaMgbOnirSoKnB9LqqVY/z6NRw5dbYYS6RUlqBcTUXkdhH5QEQWicgJETEi8kU+8kl0rutp2e9jvUtEZI6IHBGR0yKyVkSeEPF2/1OFqqioKObNm8eDDz5IQkICkZGRJCQk8MQTT7B+/XrKlrVjRTds2JDY2Nhc64sI9913H2CHq3RJT09nw4YNmf8nJSV5XRISm45cWgAAIABJREFUEjyWbdasWSQnJ9OtWzfq1asX7F1XoUo7yRbYuF8TeW32pszHnepW5tO72xEdcQ5coiOioeUd0H8uPPAztOkDETGe0+5fB988Du80gTnPwEFt3hFqRIQ3b29JlXJ22OQDyWd47uu1OsylCgnBqiJ5ERgEtAYKOvPGceDfHpb/ekosIjcDC4FLgWnACCAKGApM9LSOCm3x8fF89NFH7N+/n9TUVLZv387QoUOpXr165pCXnpreuNx7771ERkby9ddfZ45bHxERQUpKCsYYv8vkyZM95jthwgQABgwYEOQ9ViEtV1CvnWTz4uuVu3lpRlafhA61KzGqX/vQGYe+KNVoDTePgH9sgmuGQHxdz+nOHLdDZo7oCGP+BhumQUZa0ZZVeVWlXDRv3571HfT9hiS+WvZXMZZIKStYQf2TQEOgAvBQAfM6ZowZ7GHJFdSLSAXgMyAD6GaMud8Y8zT2x8WvwO0i0rOA5VEhJJCgvkaNGgwcOJAjR44wevTooGx3+/btzJgxg6ZNm3LnnXcGJU9VAjgyYN/q7M9pTX3A5m5M4ukpWc2XWtWsyOf9OlAm6hyfIqVMPFwyyA6J2WcqNLwO8NKkK3ERTO7nNmPt7qIsqfLi8sbVuKfThZmP//3NRnYd0mZTqngFJag3xsw3xmwzRX//6XagKjDRGJM53IkxJhV79wAK/iNDhZBAgnqAl156iXLlyvHmm2+Snl7wab1ff/11MjIyGDJkiI56cy45tBXOnsx6HBvvfUZRlc2vOw7zyJcryXDYr4XG1csz9t6OlI/xPFP0OSksDOpfBXdNhMfXQJcnoYyX+S9OJmXNWDuhF2ybCw5H0ZZXZfP89U2oX81OKpaSlsETE1eRnqHviSo+oRidRItIHxF5XkQeF5HLfbSNv8L59zsPry0ETgOXiEi0v42KyApPC9A4f7uhgu3IkSPs3m1rqfwF9dWqVWPs2LH07ds3c538cjgc1KtXj7fffjvgSapUKbFnRfbH57fTTrIBWLv7GAPGLudsug1wLqxchrH3dySujAb0XlW6EK4abMe8v20U1OrkOZ1xwJY5MP52GNYaFg+FU4eKsqTKyQ5z2ZrIcHtNWLP7OKMWe58jRanCFor3QKsD43I8t0tE7jXG/Jzj+UbOv1tzZmKMSReRXUAzoC6wKWcaVbK4aumrVKlCjRo1/Ka/9dZbufXWWwu83bCwMJ5//vkC56NKIE9BvfJp+4Fk+n6+lJNn7B2yhArRfHH/RVQr76VzqMouIhpa3G6XpA2wbBSs/Sr7HSOXY3/AvMEw/z92bPz298GFl+gPzyLUrEYcT1zVkLe/t52a3527laubJlC3arliLpk6F4VaTf1o4EpsYF8WaAF8AtQGvhWRnNWzcc6/x73k53q+or8NG2PaeVqAzXncB1VILr/8cowxHDyo4wKrIqJBfZ7sPnqau0ct5ehp26mzYplIxt1/ETXjyxRzyUqohGbwt3fhn5vhhnchIfcwvoAdFnP9FBhzPYy4CH77GFKOFm1Zz2EPXFo3c7bZM+kOnp26DodDR8NRRS+kgnpjzL+NMT8ZY5KMMaeNMeuNMQ8C7wKxwOA8ZumqrtBPl1Iqb9JScs8kq0G9V4dOnuHuUUvZdzwVgDJR4Yzu14GGCeWLuWSlQHR56HA/PLgY7vsBWvaEcC+tSg9tge/+ZYfFnP4w7F6uk1oVssjwMN66vSURYTbkWJp4hPFL/yzmUqlzUUgF9T587Pybc1YgV018HJ5VyJFOKaUCs28tONw6WVeqDWUrF1txQtmpM+ncN2ZZ5ugfUeFhfHp3e9rUqlTMJStlRKDWRfD3T+ywmFe/6n1YzPQUWD0eRl4JH3eFZSMh9UTRlvcc0qxGHA9eljV/yRtzNrHnWIqPNZQKvpIS1B9w/i2b43nXzBwNc64gIhFAHSAd2Fl4RVNKlUra9CYgaRkOHh6/krW7bd1JmMCwXq3p0sDLKC4qOMpWhs6P2WEx75kBTW+GMC/d5JLWwex/wjuNYeajsHdV0Zb1HDHoivrUq2rDlFNnM3hh2jqdlEoVqZIS1LuGAcgZnP/k/Huth3UuBcoAvxhjzhRWwZRSpZQG9X4ZY3h26jp+3prVz+XVW5pzbfPzirFU55iwMKjbDe4YC09ugCtehLiantOmnYKVY+HTbvDJpbD8cziTXISFLd1iIsN56/aWmf2UF2w5yLRVBZ2PU6nAFXlQLyKRItJYROrleL6ZiMR7SH8hMNz58IscL08BDgE9RaS92zoxwGvOhx8FrfBK5ZHW0pRgGtT79d8ftjB1ZdaQsf/P3n1Ht12dfxx/X+84TpzlbGcnzt6TFSAEwqZAmKWUTgo07A46gO7+WGGW/n60pUALYe+dhLACIcPZO3FiZznDjhOPeOj+/vjKkr6yleHIkix/XufoyPer+5WenNPaD1fPfe6M0/tx9YSeh7lDGlWrznDKnU7P+6tedA61MiH+zO9YCm/fCvfnwJsztHofJmN6tuPaSb1849+9vYrdB7SuKJERlpaWxpiLgNoG3p29z5OMMU97f95jrb3D+3M3nPaSW3C62tSaDvzCGDMX2AwcAPoC5wJpwLuA61RZa22JMeaHOMn9J8aYF4B9wAU47S5fBmaF4994tIwxWGvxeDw6pEh8Sb1Ri7mmpWwfFAX0mzaJ0Hl49OKJQc/Oz+PxuRt948vGdufWqXUqISUaEhJhwFnOY3+Bszq/+Bk4sKPu3KpSWPxv59FlBIy+FoZNh7TWdefKUbnzrBw+Xr2LgqJyisuquOfNlTx+9ehohyXNQLiyzpHAtd7HWd5rfQKuXXoU7zEXeA2nDv4q4DZgMvC59z3Os9ZWBt9krX3dO+9T4BLgp0CV9/4rIn3KbXKyc7hKRUVFJD9WYlTt/w5q/3chTUTwKn2nwZCitoy13l+xk9++6e8MdFpOFn/81jD9x2ssyuwOp90Ft6yAK/4L/c/E3xguyI6l8M5t8EAOvHGjOuc0UMvUJP588TDf+J3lO5i9elcUI5LmIiwr9dbaezjKdpPW2jzq+Y3iPVgq+HCpo/38L4BzGnJvuLVq1Yq9e/dSVFREixYt9EeuGbPWUlTk9Ipu1Upt/ZqUOqU3Y+uf1wwtzNvHjBeW+HK9EdltePzq0SQn6pvJmJaYBAPPdR7FW2Hxs7Dk2RCr92Ww5Dnn0XEIjPkuDJ8OLdTN6Gid3D+L6WO689IipzztnrdWcmK/DqQlJ0Y5Moln+i0cZq1bt8YYQ0lJCdu3b6esrAyPx6Pa6maitvSqrKyM7du3U1JSgjGGzMxQXVclJqmevl6b95Tyg2cWUlntAaB3h5b889qxpKfE4uHkElKbHnD6r/yr9/2mEnL1vnAlvHen0znn1R/Dli+1en+UfnnOIDJbON/S5u8r58l5G49wh8jx0W/iMEtLS6N79+4UFBRQUlJCSYn6Ajdnxhi6d+9OamqIg2Ik9lirpL4e+0orue5fCyj2nhbbISOFf183nvYZ+t92kxW8er/kOWcF/8D2unOrK2DZC86jfX8Y/R0YeRW0VOvSUNq1TOFn03L41WsrAHjik41cPKo7PdqrlE8ah1bqG0FGRga9e/emffv2pKSkqASnmTHGkJKSQvv27enduzcZGRnRDkmORfEWKNvrHye3hKyc6MUTAyqqavjhMwvJ21sGQFpyAk9dO07JSTxp08Nbe78crpx1+M45e9fDR79xVu9fvBY2zAaPJ7LxNhFXjOvB8O7ON7WV1R7ufWvlEe4QaTit1DeS1NRUOnbsSMeOHaMdiogci+BV+q6jnG4izZTHY7njpaUs2uLsDzEGZl4+ipHZbaIcmTSKxCTImeY89m9zTqVd/Czs31p3rqcKVr3uPDJ7wKhvw6irnc25AkBiguH3Fw7loie+wFqYvaaQj1ft4ozBnaIdmsQhrdSLiATattg97ta8W9Hd/+Fa3l7m30z5q3MGMW1o58PcIXEjsxtM/hncnAvffgUGXRD61Nr9W+GTP8HMYfDcpbDqTaiu07CuWRqR3YYrxvXwje95ayUVVTVRjEjilZJ6EZFABQvd4+7Nt/PNCwu28sQn/s1910zsyfdP6h3FiCQqEhKh3xlw+bNw2xqY+jto36/+udYDGz6CF6+BBwfBB7+C3WsjG28M+tlZObRJdzbNFhSVu/5/JRIuSupFRGrVVDm9ugM1002yn63fza9eX+Ebn5aTxd3nD9YeoeYuIwtOvBluWgjXvQcjroSktPrnlu2B+Y/B4+PhH2c6ZTyHDkY23hjRtmUKP5820Dd+ct5GtuwtjWJEEo+U1IuI1CpcDdXl/nFGJ2jdLXrxRMmGwgPc8J/F1Hic1oVDurbmsatGk6Re9FLLGOh5AnzrSbh9LZxzP3QeFnp+/tfw5k3eg61ugq1fN7vWmJePzWaEdy9KZbWHe95cqXbXElb6DS0iUqu+VpbNbGW6qLSS7/97IQcqqgHo3DqNf353HC1T1VdBQmjRBsb/EK7/HH40D8b9AFJDnM1RedA59OqfZzor+F88DAcLIxtvlCQkGH5/4RDfr5S5a3cze3Xz+LdLZCipFxGpVSepb16bZCurPVz/3CK2eFtXtkhO5Klrx9KpdYjyCpFgXUfCuQ/A7WvgW/8LvU4OPXfPOvjot05rzOevgjXvOiVwcWx49zZcOd6/afZP762mqkbtQCU8lNSLiNSq0/mm+dTTW2v5zesr+HrzPt+1hy4fydBuOg1ZGiAlHUZcDt99G366GE66DTJCdE2yNbD2HXjhSnhwMHz467jeXHv71AG08n7ztWl3Kc8vqKddqEgDKKkXEQFnA9/u1e5rXZvPSv0/Pt/MrIX5vvGdZ+WodaWER/u+cMbdcOtKuOpFGHR+6NaYpYXw5aNOac5TZ8DCf0HF/sjG28jaZ6Ry4+n+7kEzP15PSUV8f0MhkaGkXkQEYEeu046vVvv+Tq1wMzBnzS7++K7/P2guHtWNG07tG8WIJC4lJsGAs+Dy55zWmGf+EbIGhp5f8A28fQvcnwOv/gg2zYubk2u/e0IvurVpAcC+0kqemKsWl3L8lNSLiED9m2SbgbU7D/DT/y7xNSIZ07Mtf75kmFpXSuPKyIITboIbvoIfzIEx10Fq6/rnVpfDslnwzAXw8AiY+ycoyotouOGWlpzIz6bl+Mb//GIz+fvKohiRxAMl9SIi0CyT+n2llXz/399QWumcbtmtTQv+fs0YUpMSoxyZNBvGQPcxcP5MpzXmkTbX7t8K8/7qJPdPnwe5/4XKptnv/YIRXV0tLu/7IH73EUhkKKkXEQEoaF5JfVWNhxv/s5iCIqcvf8uURP7x3bF0yEiNcmTSbAVurp2RC5N/DpnZoefnfQav/wTuHwCv3wh5XzSp3vfGGH5z7iDf+M2l28nNL45iRNLUKakXEdlfACUF/nFiCnQeGr14IuCP76xm/qa9vvHMK0YxsHOI8geRSGvXG067C25eBt95A4ZND31ybeVByH0Onj4HHhkFn/wVirZENt4GGturHWcHbEj/w9urdCCVNJiSehGRrV+5x11HQ1L8rljP+mYrT3+Z5xvfPnUAUwd3il5AIqEkJECfU+GSp5zynPNmQvdxoecXbYZP/gQPD/eX5xw6GKloG+Tn0waSnOjsYVm4pYgPVu6MckTSVCmpFxHJ/9o97jEhOnFEwKIt+/j16yt843OHdeGmgPZ6IjGrRRsYex384GO48Rs48ZbQve/BXZ7z2k9g86cx2T2nV4eWXDOxl2/8l/fWUFkde3FK7FNSLyKydb573GNSdOJoZDv2l/PjZxdTVeN8vT+wcyvumz5cnW6k6ckaAFPvdXrfX/0KDLkYEkN8u1ZVCkv/C/8+31nBn/172LMhsvEewYwp/chskQxA3t4y/vN10ygfktiipF5EmrdDB2DXSve17Phbqa+oquFHzyxiz8FDALRNT+b/vjOW9JQQhwCJNAWJSdD/DJj+L7hjLZz7IHQbG3r+/nz47H54bAw8NRW++QeUF0Uu3hDapKfw04BvzB6fu4GyyuooRiRNkZJ6EWneCr5xHzrVYQCkt4tePI3AWssvXlnG8m3OyZxJCYYnrh5Ddrv0KEcmEkYt2sK478MPZzvlOSfdCq26hp5fsADeuc0pz3nxO7D2PaiJ3smu10zqSddMZzPwnoOV/OuLvKjFIk2TknoRad6CN8n2mBidOBrRP7/I4/Xc7b7x3ecPZlLf9lGMSKSRZQ2AM+6BW1fAt1/1ds9pUf/cmkpY9QY8fwU8MBDe+wVsz414e8zUpERmTOnvG/993kb2l0fvPzKk6VFSLyLNW3BSnx1fSf38jXv507urfeMrxmXz7Yk9oxiRSAQlJEK/KU73nDvWwQWPQc8TQ88v2wNf/w3+dzI8MQk+fwj2b4tYuJeM6U6v9s43aCUV1Tz12aaIfbY0fUrqRaT5qqmGgoXua3G0Ur+9uJyb/ruYGo+z4jgyuw33XjhEG2OleUprDaOvgevedQ63OvWX0LZ36Pm7V8PH98BDQ+DfF3jbYx5o1BCTExO4deoA3/ifn29mr3cfjMiRKKkXkeZr13KnM0atllnQrk/04gmjiqoafvLcIvaWVgLQISOFv317NKlJiVGOTCQGtOsNp/4CZiyB730IY66DtMwQky1snue0x7yvP7zyA1j/sbMo0AjOH96VnE6tACitrOFvn2xslM+R+KOkXkSar61B/emzJ0AcrGJba/ntGytYWuDfGPv4VaPpkhmiplikuTLGOZfi/Jlw+zqY/m8YMA0SQnSFqi6H5S/Bfy6BBwfB+3eFvf4+IcFw25n+1fpnvtrCzv0VYXt/iV9K6kWk+arTnz4+Sm/+8/VWXlxY4Bv/6txBTOijjbEih5WcBkMugqtmwW1rYNpfoeuo0PNLC+Grx7319xPhswehOD8soZw5uBMjujvfHFRWe3h0zvqwvK/ENyX1ItI8WVvPSbJN/9CpRVuKuPctf9/9i0d147sn9IpeQCJNUUYWTLwefvQJ3LgATroNWncPPX/3Gph9L8wcCv86Fxb9G8qLG/zxxhhuPzPHN571TT5b95Y1+P2keVBSLyLNU/FWOLDDP05Kg87DoxdPGBQeqOAnzy3ynRg7pGtr/nTxMG2MFTkeWTlwxt1wy3K49i0Y9W1IaRV6/pbP4a0ZcH9/mHUNrH4Lqo99s+vJ/TswvrdzZka1xzLz43UN/RdIM6GkXkSap+BWlt3GQFJKdGIJg+oaDz/97xIKD/hPjH3y22NIS9bGWJGwSEiA3qfAhY/Dnevh0n8evv6+phJWvwmzvu0k+G/OgLzPweOpf34QYwx3nuVfrX8tdxvrdzVu9x1p2pTUi0jzlB9fh07d98Favt68D3D2/j1y5SidGCvSWJJbwNBLnPr729fC2fdBt7Gh51fsh8X/hqfPhZnD4KPfws4VR/yYcb3aMXlAFuBUDM78WLX1EpqSehFpnuLo0Kn3V+zg75/6D6m5feoATu6fFcWIRJqRlh1gwo/gh7Php4th8i8O3/++pAC+eBiePNE54OqzB5xywBDuCKitf3fFDjYUarVe6qekXkSan/JiKFztvpY9LjqxHKdNuw9yx0vLfOMpAztyw6n9ohiRSDPWvi+c9kun//33P4ZxP4T0w3SeKlwFs3/nrN7/cxp88xSU7nVNGdY9k9MHdgSc1fon5qpvvdRPSb2IND8F3wABfaU7DoYWbaMWTkOVVVbzk+cWc/CQcwhOdrsWPHjZSBIStDFWJKqMcRYKzr3fKc+56iUYNh2SD1MSt3U+vHM7PDAA/nMZLHsJDh0E4KbT/f+h/sbS7WzZWxrqXaQZC7G7Q0QkjgX3p8+eEJ04joO1ll++upy13o1zqUkJ/O3qMWSmJ0c5MhFxSUyGAWc6j0MHYe27sOxF2DgHbE3d+Z5qWP+B80hOh5xzGD1sOpP7ZjJv435qPJa/fbKRv1zStLt1SfgpqReR5if4JNkmuEn22a+28Ebudt/49xcNZWi3UMfci0hMSM2A4Zc5j4O7YdXrToJfsKD++VVlsOJlWPEyT6W04aWk0bzpOYFXF1t+OqU/3drolGjxU1IvIs1LdSVsW+S+1sSS+iVbi/j926t84yvHZ3PZ2OwoRiQixywjC8b/0Hns2+wk78tegj1r652eXFnMVUlzuIo57LRt2fSfM+l20fXOqbc6i0JQUi8izc3OZVBd7h9ndIY2PaMXzzEqKq3kxv8s9h0wNaxbJnefPyTKUYnIcWnXG065E06+A3atgOUvwfJXnE459ehsiui8exb83yxo18dprzn0Uug4MMKBSywJy0ZZY8ylxphHjTGfGWNKjDHWGPPcMb5He2PMD4wxrxljNhhjyo0x+40xnxtjvm+MqROrMaaX97NCPV4Ix79PROJIcCvLHhObzCqXx2O57cVctu+vAKB1WhJPXD1aB0yJxAtjoPMwmPo75wTb696Dsd+DFu1C37NvE3x6HzwxAZ44wWmRuW9z5GKWmBGulfpfAyOAg0AB0JD/VJwO/A3YAcwFtgKdgIuBp4CzjTHTrbW2nnuXAq/Xc/3IJzuISPMSvEm2CZXe/G3eRuau3e0bP3jZSB0wJRKvEhKg5wnO4+z/gY1zYcXLVK96i6TqsvrvKVwJs1c6bTK7jYVJNzir+NIshCupvxUnmd8ATMZJyo/VOuAC4B1rre8MZWPMXcAC4BKcBP+Veu7Ntdbe04DPFJHmxFrID9ok20Q633y1aS8PfOivtf3x5D6cMbhTFCMSkYgJ6KCTeF4pf3r4YcaUzObUhFxSTXX992xbCC9/DwrXwGl3NZlvJKXhwlJ+Y62da61dH2IV/WjfY4619q3AhN57fSfwpHd46nGEKSLN3d4NUOpf6SY53fmqO8YVHqjgp88vweP9DTuuV1vXKZMi0nyYlJaMnHYdP666jXGH/sav7U+o6nUamBBleJ/+D3x8t7OoIXGtqWyUrfI+h/jPUboaY34MtAf2AvOttctCzBWR5mrzp+5x9gRnBSyG1XgsNz+fy+4DhwBo3zKFR68cTXKizg4Uaa6mDelMv44ZbCiE5w6dTIfu3+OWS9s6LTJXvFK3zPCLh53OX9P+rBX7OBbzfxWMMUnAd7zD90NMm4qzmv9H7/NSY8xcY0yPY/icRfU9aNj+ABGJRXmfuce9T45OHMdg5sfrmL/JOTbeGHj4ilF0zkyLclQiEk0JCYYbT+vrGz/9ZR5lKW2d9pjfex9+MBvSgs6t+Ppvzom1Hg8Sn2I+qQf+AgwF3rXWfhD0Whnwe2AM0Nb7qK3pPxWYbYxpGblQRSRmWQt5n7uv9TolOrEcpXnrdvPY3A2+8c1T+nNS/w5RjEhEYsX5w7uS3c45fKq4rIqXFwW0v+w+Fr7zJrRo675p4T/grRngqeckW2nyYjqpN8bMAG4H1gDXBL9urS201v7WWrvYWlvsfXwKnAl8DfQDfnA0n2WtHVPfw/vZItLU7V7jrqdPyYCuI6MXzxHs3F/BrbNyfWWwJ/XrwE9P7x/doEQkZiQlJvD9E3v7xk99tpkaT0DdfNeR8N13ID1oIWDJs/D6DUrs41DMJvXGmBuBh4FVwGnW2n1He6+1thqnDSZAbC/FiUhkBNfT95gUs/X01TUeZrywhH2llQB0bJXKzCtGkpigWlgR8btsXDaZLZzfY1v3lfHByp3uCZ2GOIl9RlCnrGUvwLIXIxSlREpMJvXGmFuAx3D6zJ/m7YBzrGqX5FR+IyJ1k/oYrqd/ePZ6Fmx21jESDDxy5Sg6ZKRGOSoRiTXpKUlcM9F/IvbfP91EnUaEHQfCd9+FVl3d11fU1yFcmrKYS+qNMT8HHgJycRL6wga+Ve2JMpvCEpiINF0eD2z5wn2tV2wm9Z+v3+Oqo7/ljAFM7NM+ihGJSCy79oRepCQ56dzS/GK+ySuqO6lDP7j8Wfe1wtURiE4iKeJJvTEm2Rgz0BjTt57XfoOzMXYRMMVau+cI7zXBGJNSz/XTcQ7EAnguDGGLSFO2awWUB/yhS82ELiOiF08IhSUV3DJria+O/sR+7bnxtH7RDUpEYlpWq1QuGd3NN/7fTzfWP7HzcEgI6GReUgAVJY0cnURSWPrUG2MuAi7yDjt7nycZY572/rzHWnuH9+duwGpgC9Ar4D2uBX4H1ACfATNM3V6qedbapwPGfwWGGGM+wTnRFmA4cLr3599Ya79s6L9LROJEcCvLXidCQoiDWqKkxmO5+YVc9hx06uizWqUy8/JRqqMXkSP6/kl9eH5BPgAfry5kQ+FB+nXMcE9KSoF2fWGP/2Rqdq+B7PERjFQaU7gOnxoJXBt0rY/3AU4CfweHV7uFOxG4JcScecDTAeNngW8B44CzgWRgF/Ai8Ji19rPgNxCRZmhzcFIfe6U3j8xe7+5Hf/lIslqpjl5EjqxfxwzOGNSJj1fvAuCpzzbxl0uG153YcZA7qS9cpaQ+joSl/MZae4+11hzm0Stgbl7wtaN8D2OtPTXonn9Ya8+z1vay1mZYa1OttT2stZcroRcRwGnbtiXoC7sY2yT75YY9PDJnvW884/T+nNBP/ehF5Oj96JQ+vp9fXbyNwgMVdSd1HOweF6prdzyJuY2yIiJhtWMpHNrvH7doBx2HRC+eIHsOHuLmgH70k/q0Z8YU9aMXkWMzrldbRma3AaCyxsMzX26pO6njQPe4cFUEIpNIUVIvIvGt3nr62PjV5/FYbn9xKbsPHAKgfcsUHlY/ehFpAGMMPw5YrX/2qy2UHqp2T6qzUq8OOPEkNv6yiYg0ljr19LFzHt1Tn29i3jr/KbcPXj6Sjq3TohiRiDRlZw7pTM/26QDsL6/ipYX57glte0NiQNPA0kIo3RvBCKUxKakXkfhVUwVb57uvxUg9fW5+Mf/zvn/D2o8n92HygKwoRiQiTV1iguEHJ/X2jZ/6fDM1noDDqBKToEOO+6bdWq2PF0rqRSR+bc+FyoN265AtAAAgAElEQVT+ccssyBoYen6ElFRU8dPnF1Pt/WM7MrsNd5yZc4S7RESO7NIx2bRNTwagoKic2d6OOD4dB7nHKsGJG0rqRSR+5X3qHvc6yekXGUXWWn756nLy95UD0Co1iUevHEVyon4di8jxa5GSyJXje/jGT3+Z555QZ7Oskvp4ob8iIhK/YrA//Qvf5PPOsh2+8V8uGU52u/QoRiQi8ebbE3v6Ntx/uXEva3ce8L+ozbJxS0m9iMSn6krY+pX7Wu/J0YnFa92uA9zz5krf+MrxPTh3eJcoRiQi8ahrmxacNaSTb/zv+Xn+F4PLb3avxtdTV5o0JfUiEp+2LYTqcv+4VRdo3zdq4VRU1XDTfxdzqNoDwIBOGfz2vMFHuEtEpGG+e4J/w+yriwvYX1blDDJ7QHLAt4PlRXAwqO5emiQl9SISn+orvYliPf0f3lnFul3Opt3UpAQeu2o0LVISoxaPiMS3cb3aMqhLawAqqjzMWrjVeSEhoW7DAB1CFReU1ItIfAo+dCqKrSw/WLmT577a6hvfff4QBnRqFbV4RCT+GWO47oRevvEz87f421vWqatfE7nApNEoqReR+FNVAfkL3NeitEl2e3E5P3t5mW88bUhnrhyfHZVYRKR5uWBk1/rbW9bpgKOV+nigpF5E4k/+V1BzyD/OzIa2vSIeRo3HcuusXPaXO7WsXTPT+MslwzBRbqspIs1DWnIiV9TX3lK96uOSknoRiT8bZrvHvSdHpZ7+ibkb+HrzPgASDMy8YhRt0lOOcJeISPjU294yK7gDzhp1wIkDSupFJP4EJ/X9pkQ8hEVb9jFz9nrfeMaU/ozv3S7icYhI89atvvaWrbtCaqZ/UuVB2J8f8dgkvJTUi0h8KdkBhf5e8JgE6HNqREPYX17FjOdzfZvSxvVqy02n9YtoDCIita6d1Mv386uLC9hfXq0SnDikpF5E4svGOe5x19GQHrkVcmstd722nG3FTo/81mlJzLxiFEmJ+nUrItExvne7uu0t62yWVVLf1OmvjIjElw0fu8f9zojox7+0qIB3lu3wjf96yXC6tWkR0RhERALV197SE1xXr6S+yVNSLyLxw1MDm+a6r0Wwnn7znlLuedNf+nPl+GzOHtYlYp8vIhJKcHvL3ENBv5t2K6lv6pTUi0j82J7rHHleKy3TKb+JgMpqDze/sISyyhoA+ma15DfnDT7CXSIikZGWnMhlY/1nZDyzIegbxN1rnYURabKU1ItI/AguvelzGiQmReSjH/p4HcsK9gOQnGh4+IpRpKdE5rNFRI7GlQE969/cUEVNi/b+F6sroCgv8kFJ2CipF5H4sTE6rSy/3LiHJ+dt9I1/Pm0gQ7tlHuYOEZHI69WhJSf2cxJ5j4VtKb3dE1RX36QpqReR+FBeBAXfuK/1bfykvqi0kttmLfWd23Jy/w5878Teh79JRCRKrp7Q0/fzVwey3C8qqW/SlNSLSHzYNA+sxz/OGgSZ3Rr1I621/OLVZewsqQCgXcsUHpg+goSEyJ9eKyJyNKYO7kSHjFQAcg91db9YuCoKEUm4KKkXkfgQhdKbF77J54OVu3zj+y4dTsfWaY3+uSIiDZWcmMBlY7sDsM4TtPCxe00UIpJwUVIvIk2ftbAh6NCpRk7qNxQe5N63/O0rvzOpJ1MGdTrMHSIiseHK8T0wBtbZ7u4X9qyD6sroBCXHTUm9iDR9u9dCSYF/nNQCepzQaB9XWe3hlllLqKhyyn0GdMrgrnMGHeEuEZHYkN0unVP6Z1FCBjtswInbnmrYtzH0jRLTlNSLSNMXXHrT60RIbrwymAc/WseKbSUApCQm8PAVo0hLTmy0zxMRCberJjjtLdcHl+Bos2yTpaReRJq+4P70/c5otI/6cuMe/v5pQPvKswcyqEvrRvs8EZHGMGVgRzq1TmWtzXa/oKS+yVJSLyJNW1U5bPnSfa2RWlkWl9VtX3ndCb0a5bNERBpTUmICl4/rUbeufreS+qZKSb2ING1bvnBOQqyV2QM69A/7x1hr+dVrK3ztK9umJ3O/2leKSBN2xbhs1gev1O9cHp1g5LgpqReRpm1DcCvL08GEP9F+ZfE23lm+wzf+yyXD6aT2lSLShHVt04Iu/UdTbQPSwaI8KC+OWkzScErqRaRpC07qG6H0ZsveUu5+Y4VvfOX4Hpw1pHPYP0dEJNKmT+rPBhu0WXbnsugEI8dFSb2INF3F+bBnrX9sEqHP5LB+RHWNh1tm5VJaWQNAnw4t+c15al8pIvFh8oCObErq5764Y2l0gpHjoqReRJquDR+5x9njIS0zrB/x6JwNLNnqfBWdlGB4+IpRpKckhfUzRESiJTHBkN5rjPvi9tzoBCPHRUm9iDRda99zj8PcynLRliIenbPeN7516gCGdQ/vfzSIiETb4NEnucZV25TUN0VK6kWkaTp0EDbNc1/LOSdsb3/wUDW3zsrF421fOb53O66f3Dds7y8iEis69h+HB3+DgaSijXDoQBQjkoZQUi8iTdOmuVBzyD9u0xM6hq/W/d43V7J1XxkArdKSePCyESSqfaWIxKPUDEozevuGBotnuzbLNjVK6kWkaQouvRl4bthaWb63fAcvLSrwjf9w0VC6t00Py3uLiMSi4Lr6ravmRykSaSgl9SLS9HhqYN377ms5Z4flrXfur+CXr/kPX7lgRFcuHNntMHeIiDR9iV1HusZ71i2IUiTSUGFJ6o0xlxpjHjXGfGaMKTHGWGPMcw18r+7GmH8aY7YbYw4ZY/KMMTONMW0Pc89gY8yLxphCY0yFMWatMeZeY0yLhv+rRCRm5S+Asr3+cVom9Jh03G/r8VjufHkpxWVVAHTNTOP3Fw097vcVEYl5XUa4hpnFKzlQURWlYKQhwrVS/2vgJmAksK2hb2KM6QssAq4DFgAPAZuAm4H5xpj29dwzAfgGuAj4GHgYKAF+C3xkjEltaDwiEqPWvuse9z8TEpOP+23/9WUen63fAziVPA9ePpLMFsf/viIiMa/LcNewD9t4f8mmKAUjDRGupP5WYADQGvjJcbzPE0BHYIa19iJr7S+stafjJPc5wB8DJxtjEoF/AenApdbaq6y1PwcmAK8AJ3pjE5F4ElxPH4auN2t3HuCv76/xjX98Sl8m9qmzjiAiEp/SMqFdH98w0VgWL/g8igHJsQpLUm+tnWutXW+ttQ19D2NMH+BMIA94POjlu4FS4BpjTMuA65OBQcCn1to3A+LxAD/zDq83Jky750Qk+vash73+3vEkJEO/Kcf1loeqa7j5hSVUVnsAGNK1NbdNHXBc7yki0uR0cdfVJxUuY0PhwSgFI8cqljbKnu59/tCblPtYaw8AX+CsyE+s556gHXNgrd0ErAN6An2CXw9mjFlU3wMYeOz/FBFpNMGlN71OOu5TZB/4cB1rdjo9mVOTEnj4ipGkJMXSr0cRkQgIqqsfZjbzckAnMIltsfRXK8f7vC7E67VLc4HLZw25R0SasjCX3ny5cQ//95m/bvSucwbRr2Or43pPEZEmKSipH5qQxyuLC6iu8YS4QWJJUrQDCFC71LY/xOu119sc5z31staOqe+6d7V+9JHuF5EIKN0D+V+7r+VMa/Db7S+r4vYXl1JbODh5QBbfmdTzOAIUEWnCgpL6/qaAkgMHmLduN1MGdYpSUHK0Ymml/khq6+KPpW6/IfeISKxa/yEEVud1HgZtejT47X7zxgp27K8AoG16MvddOhxtwRGRZiu9net3arKpIcfk89JCleA0BbGU1Neuqocqjm0dNK+h94hIU7XmHff4OEpv3sjdxptLt/vGf754GB1bpzX4/URE4kLQZtmhCXl8vHoXew8eilJAcrRiKalf630OVf/e3/scWD/fkHtEpCmqqoCNc9zXGniK7Lbicn79+grfePqY7kwb2uV4ohMRiQ/BdfVmM9Ueyxu520PcILEilpL6ud7nM40xrriMMa1wes6XA18FvFT7F75OUa23ReYAYAvOAVYi0pRt/hSqyvzjVl3rrCgdDY/HcvuLuRyoqAYgu10L7r5gSLiiFBFp2uqs1G8G4LUlDT5bVCIk4km9MSbZGDPQe3qsj7V2I/Ah0Au4Mei2e4GWwDPW2tKA6/OA1cApxpgLAj4jAfird/jk8fTPF5EYEdzKMuds59jXY/TU55v4atM+ABIMPHTZSDJSY6lngIhIFAWt1A80+SRTzfJt+9lQeCBKQcnRCMtfMmPMRcBF3mFn7/MkY8zT3p/3WGvv8P7cDScR34KTwAe6AfgSeMQYM8U7bwJwGk4Jza8CJ1tra4wx1+Gs2L9sjHkZ2ApMAcbi9LZ/KAz/RBGJJo8H1gUdR9GAevrVO0q4/wN/Nd4Np/ZjbK92xxudiEj8yMiC1t2gxFmZTzHV9DcFrLK9eG3JNu48S8f3xKpwrdSPBK71Ps7yXusTcO3So3kT72r9WOBpnGT+dqAv8AgwyVq7t557vgbGAW/gnEh7K87G2d8BU6212tkh0tTtWAIHdvjHKRnQ++RjeouKqhpueSGXSm+/5WHdMrn5jP5HuEtEpBkKUYLz+pLteDwqfohVYVmpt9beA9xzlHPz8LearO/1fOC6Y/z8VcD0Y7lHRJqQ4K43fU+HpNRjeosHPlzL2l3OV8dpyQk8dPlIkhNjaVuRiEiM6DIC1vp/745J3sqLNU6TgW/y9jGhT/soBieh6C+aiMQ2a2Hl6+5rA889prf4cuMenvp8s2/snBqbEY7oRETiT1Bd/aT0fN/Pr+dqw2ysUlIvIrFt53LYt9E/Tkw5plaW+8uruCPo1NhrJurUWBGRkLq6y2+6H9pIIjUAvL1sBxVVNdGISo5ASb2IxLaVr7nHfadAWqjz5ur67Rsr2K5TY0VEjl6rzpDRyTdMqDnEiW2cbY0HKqqZu6YwWpHJYSipF5HYZW3dpH7It4769jeXbncdmKJTY0VEjlLQZtmruu/z/fyqetbHJCX1IhK7di6DIn8tPImpR116s724nF+/ttw3vmS0To0VETlqderq/Yn8J2sLKSqtjHREcgRK6kUkdgWv0vebAmmtj3ibx2O58+WllHhPje3etgX3XDC4MSIUEYlPQUl9ZvEqRmS3AaCqxvL28h313SVRpKReRGLTcZTe/OvLPL7Y4NR/GgMPXjaSVmnJ4Y5QRCR+BW2WZcdSLhnhr7N/XSU4MUdJvYjEph25UJTnHyemwoBpR7xt3a4D/PX9Nb7x9ZP7Mr63To0VETkmrbu5NstSVcYFXYpISnAaDSzaUsSWvaVRCk7qo6ReRGJTcG/6/lOPWHpTWe1xTo2tdk6NHdylNbeeMaCxIhQRiV/GQPZ416U2e5YweUCWb/z6ku3Bd0kUKakXkdhTX+nN4IuOeNtDH69j1Y4SAFKSEph5xUhSkvRrTkSkQbInuMf5X3HRqG6+4WtLCrC1h4BI1OmvnYjEnu1LoHiLf5yYCjmHL735Jm8fT87zH1L182kDGdCpVWNFKCIS/+ok9QuYOrgTGalJAOTtLSM3vzgKgUl9lNSLSOwJXqXvPxVSQyfoByqquHVWru/U2BP7tee6E3o1XnwiIs1BlxHOokqt/fmkle3k7KGdfZe0YTZ2KKkXkdhiLawKqqc/Qteb3721ioKicgBapyVx//QRJCTo1FgRkeOSlApdR7mvFSzgWwElOO8s30mNRyU4sUBJvYjElu2LoXirf5yUBgPOCjn9/RU7eWlRgW/8h28No0tmi8aMUESk+QjaLEv+Aib0aU+HDGcFf8/BQ3y9aW8UApNgSupFJLYcQ+lN4YEKfvnqMt/4wpFduWBE18aMTkSkealTV/81iQmGc4f5S3DeWqYuOLFASb2IxA5rYeUb7mshSm+stfzs5WUUlVUB0CUzjd9dMLSxIxQRaV6CV+p3LIXKMs4PWEB5b8VOqmo8EQ5MgimpF5HYsW0x7A8qvelff+nNf77eyidrd/vGD0wfQWa6To0VEQmrjI7Qtrd/7KmG7UsY3aMtXTLTACguq+LzDXuiFKDUUlIvIrFj5avucf8zITWjzrRNuw/yx3dW+8bfP6k3J/Tr0NjRiYg0T/WU4CQkGM4b3sV36a2lKsGJNiX1IhIbaqph+Uvua0PqHjhVVePh1lm5lFfVADCgUwZ3npUTiQhFRJqnejbLAq4SnI9W7qLC+3tZokNJvYjEhs2fwMFd/nFKKxhwdp1pj83ZwNKC/QAkJxoeunwkacmJEQpSRKQZ6jHRPc7/GqxlWLdMerRLB+DAoWrmrdtdz80SKUrqRSQ2LH3BPR5yIaSkuy4t2VrEY3M3+Ma3Tc1hSNfMSEQnItJ8ZQ2E1Nb+cfk+2LsBYwznj1AJTqxQUi8i0VdRAqvfdl8bcaVrWFZZzW0vLvUdcjK+Vzt+dEqfSEUoItJ8JSRC97Hua/lfA+4SnNmrCymrrI5kZBJASb2IRN/qN6G63D/O7AE9TnBN+cM7q9m8pxSAjNQkHrhsBIk6NVZEJDLq2SwLkNOpFf07Og0NyqtqmL26MNKRiZeSehGJvtzn3eMRl0OC/9fTnDW7+O/X/laX91wwhOx27tIcERFpRCE2yxpjOG+4f7VeJTjRo6ReRKKraAts+dx9bfgVvh/3HjzEz15e7htPG9KZS0Z3i1R0IiIC0G0sEPDt6O41UF4EwHkBdfWfrNtNSUVVhIMTUFIvItG27EX3uPs46NAPcE6N/cWry9lz8BAAWa1S+dPFwzBGZTciIhGV1ho6DXFfK1gIQN+sDIZ0dTbSVlZ7+GjlruC7JQKU1ItI9FgLS4NLb/yr9C8uzOejVf4/DvddOpx2LVMiFZ2IiAQKrqvf+pXvR1cJzjKV4ESDknoRiZ6ChbBvo3+ckAxDLgZgy95S7n1rle+l70zqyak5HSMdoYiI1AqxWRZwnS77+fo9FJVWRioq8VJSLyLRE7xKnzMN0ttR7T01tqzSOZ2wT1ZLfnn2oCgEKCIiPsGbZbctck4DB7LbpTOqRxsAqj2W91fujHR0zZ6SehGJjupDsOIV9zVvb/q/fbKRxVuLAUhKMMy8fCQtUnRqrIhIVLXtBS0DvjGtKoNdK3zDwBKct1WCE3FK6kUkOtZ9ABXF/nGLdtBvKssKinl49nrf5Zun9Gd49zZRCFBERFyMCdnaEuDcYf4SnK827WOfSnAiSkm9iETH0hfc42GXUu5J5JZZuVR7T40d3aMNPzm1bxSCExGRetWpq/dvlu2cmcZobwlOjcfy0SqV4ESSknoRibzSvbD+A/e1EVfwp3dXs2m3c2psy5REHrp8JEmJ+jUlIhIz6iT1C1zDs4f6V+vfW6GkPpL011JEIm/FK+Cp9o87DGBuSXee/WqL79Jvzx9Mz/YtoxCciIiE1HUkJAa0Ft6fD8X5vuG0oZ19P3+xYQ/7y3UQVaQoqReRyMt9zjUsHXQZd77iPzX2zMGduGxsdqSjEhGRI0lK9Z4uG2DzPN+P2e3SGdYtE4CqGsvs1TqIKlKU1ItIZG1bDDuW+oYWw++2DPGdGtshI5U/69RYEZHY1Weye7xpnmsYuFqvEpzIUVIvIpG16F+u4Y6sk5i1zvrG900fTvuM1EhHJSIiR6t3UFK/eZ5zQrjX2QFJ/bx1uzl4qBppfErqRSRyKkpgubs3/R93TfT9fM3EnpymU2NFRGJbtzGQHLDn6eAu2L3WN+yTlcHAzq0AqKz2MHdNYaQjbJaU1ItI5Cx/EapKfcM9Ce15v3I44Jwae9c5OjVWRCTmJaVAzxPc1za7S3ACu+C8rxKciAhbUm+M6W6M+acxZrsx5pAxJs8YM9MY0/Yo7z/VGGOP4pEddN/h5n4V6vNEJMKshYVPuy49VzmZGhJJSjA8fPkonRorItJU1Kmr/8Q1PHuYvwRnzppCyitrIhBU85YUjjcxxvQFvgQ6Am8Aa4DxwM3ANGPMidbavUd4mzzg3hCvDQMuBlZaa/PreX0L8HQ91wuOGLyIRMa2RbDL3+GmxhpeqD4NgFunDmBY98xoRSYiIscquK4+73OoqYZEJ7Xs3zGDPlkt2bS7lPKqGuat2+3aQCvhF5akHngCJ6GfYa19tPaiMeZB4Fbgj8D1h3sDa20ecE99rxljnvf++L8hbs+z1tZ7r4jEiIXuDbJzPKPYSXvG9mzL9ZN1aqyISJPSaSikt4cy75rtoRLYkQvdnXaXxhjOGdqFx+ZuAOD9FTuU1Dey4y6/Mcb0Ac7EWWl/POjlu4FS4BpjTINOkTHGtAe+BZQDzzY8UhGJmvJi58CpAP+tmUJGahIPXT6SxAS1rxQRaVISEqD3Ke5rQSU4gUn87NWFHKpWCU5jCkdN/ene5w+ttZ7AF6y1B4AvgHRgYvCNR+m7QCrwkrW2KMScNsaY7xlj7jLG3GiMaehniUhjWPYiVJf7hgW2A/M8I7j3giFkt0uPYmAiItJg9bW2DDCka2uy27UA4MChar7YsCdSkTVL4Ujqc7zP60K8vt77PKCB7/8D7/PfDzNnBPAPnDKfx4D5xphcY8ywo/0QY8yi+h7AwAbGLSLgbJAN6k0/q/pUzh7WjYtHd4tSUCIictyCN8tu/Rqq/As4tSU4td5bri44jSkcSX3t7rb9IV6vvd7mWN/YGDMZJ6leaa39MsS0B4ETgSygFTAOeBkn0Z9jjFHWIBJN+QugcJVvWG0TmJs+jT9+a6hOjRURacra9obMHv5xzSHI/9o1JbAE58NVu6iqcRV1SBhFok997V9te9hZ9fuR9znkKr219nZr7ZfW2j3W2oPW2oXW2unAK0AH4I6j+SBr7Zj6HjidfESkoYJW6Wd7RvPLy0+jTXpKlAISEZGwMAb6HL6ufkT3NnTJTANgf3kVX206UjNEaahwJPW1K/Gh+tG1Dpp3VIwx7YBLaPgG2Se9z6ccdpaINJ7yIjwrXnVd2jfoKk7s1yFKAYmISFj1Oc093uSuq09IMK7V+vd0EFWjCUdSX3sucKia+f7e51A196Fci7NB9kVrbXED4trtfW5Q1x0ROX7VS/5LQs0h33hnQkcunv6dKEYkIiJhFdwBZ0eu0/EsQODpsh+u3EmNpyHFG3Ik4Ujq53qfzzTGuN7PGNMKp969HDjW011/6H0O1Zv+SGo74Gxq4P0icjyspfhTd+Vc4tjrSE1OjlJAIiISdhkdoeNg/9h6nIOoAozp2ZYOGU7J5Z6DleTmh2pmKMfjuJN6a+1G4EOgF3Bj0Mv34qyUP2OtLa29aIwZaIwJ2VXGGHMyMAhYcZgNshhjRtfX/94YMxynEw7Ac0f5TxGRMFr12at0qNjiG3tMElknfz+KEYmISKM4QmvLxATDlIGdfOMPV+2KRFTNTrg2yt4AFAKPGGNeN8b82RgzB+c02XXAr4Lmr/Y+QqndIHukVfoZwA7vZz5qjLnfGPM2sBhoD/wf8Pxh30FEwq64rJKSuY+4rpnBF0KrTiHuEBGRJiu4tWVQXT3A1MH+3/8fKalvFGFJ6r2r9WOBp4EJwO1AX+ARYJK19qi3Ohtj2gKXcnQbZF8HPgaG4tTgzwDGAO8BF1prf2StVeGWSARZa3nk+TeZaHNd182k4C/yREQkLvQ8EUyif7xnLZTscE05qX8HWiQ7czbtLmVD4cFIRtgsJIXrjay1+cB1Rzk3ZHNq76mxLY7yfV7HSexFJEa8tKiA/pufc/92yZ4A3cdELSYREWlEaa2h2xgoWOC/tvlTGHG5f0pyIqcM6MAHK51V+o9W7aJfx4xIRxrXItGnXkSaibw9pTz85nwuTnRvkmLiDdEJSEREIqNOCc4ndaZMHexvbfnRKrW2DDcl9SISFlU1Hm6ZlcvFNR+Qaqr8L2T2gIHnRS8wERFpfPVtlg2qgJ4ysCMJ3lqNJfnFFB6oiFBwzYOSehEJi0dnr2dV/m6+k/SR+4UJP4bEsFX6iYhILMoeD0kB1dMl22DvBteUti1TGNerHeDk+7NXF0YywrinpF5Ejts3eft4bO4Gzk+YT5YJODw6JQNGXxO9wEREJDKSUqHnJPe1dR/UmaYuOI1HSb2IHJf95VXc8kIuHmv5ftJ77hdHXQNpmdEJTEREIqv/We7x2vfqTDkzoK7+8w17KD1U3dhRNRtK6kWkway1/Oq15WwrLmdSwioGJ2wJeNU4pTciItI85Exzj7fOh7J9rks92qczsHMrACqrPXy6bnekoot7SupFpMFeWbyNt5c5vYi/lxi0IjPwXGjXOwpRiYhIVLTtBR0H+8e2BjZ8XGeaSnAah5J6EWmQvD2l3P3GCgB6mR1MSVzinqDDpkREmp+cs93jte/WmRKY1M9ZW0h1jaexo2oWlNSLyDGrqvFw8wtLKK2sAeCWjNkkENC6rMtI6DEpxN0iIhK3BgQl9RtmQ3Wl69Kwbpl0bp0GQHFZFd/kFUUqurimpF5EjtnMj9extMDpcpOVeJDz7SfuCZNuBBPy4GgREYlX3cZAyyz/+FAJbPnCNcUY41qt/1AHUYWFknoROSbzN+7liU82+sZP9vuGxOoy/4RWXWDwRVGITEREoi4hAQYEdcFZ936dacF19TbooCo5dkrqReSoFZdVcuusXN8hgWf0SWP0zlnuSRNvgKSUyAcnIiKxIecc93jtu3VOl53Ypz2tUp2DCQuKylmz80CkootbSupF5KhYa/nFK8vZWeIc6902PZmHen+DOVTin9SiHYz9XpQiFBGRmNDnVEhM9Y+Lt0LhateUlKQETh3Y0TdWF5zjp6ReRI7K8wvyeX+lv+7x/gv70Wrx392TJt0AqRkRjkxERGJKSksnsQ90hC44qqs/fkrqReSI1u06wL1vrfSNvz2xB1NK34XygENFUlvDuB9GIToREYk5wQdR1XO67Kk5WSQnOk0VVmwrYcf+8khEFreU1IvIYVVU1TDj+SUcqnb6COd0asWvz+oDXz7qnjj+R9CiTRQiFBGRmDMgKKnftggOuEtsWqclM6F3e9947hqdLphrs1oAACAASURBVHs8lNSLyGH9+d3Vvg1MqUkJPHLlKNJWPA8HA74qTU53NsiKiIgAtO4KXUcFXLCw/oM6004PqKufs0Z19cdDSb2IhPTRql38e/4W3/g35w0mJysNPp/pnjj2e9CyPSIiIj7BB1GtrdvaMjCp/2LDXiqqaho7qrilpF5E6rVzfwV3vrzUNz5rSCeuntADls2C/fn+iYmpcMJPoxChiIjEtJygpH7jHKhy18336tCSPlktASivqmH+pr2Rii7uKKkXkTpqPJZbZ+VSXFYFQJfMNP56yXCM9cBnD7gnj/4OtOochShFRCSmdR4Grbv7x9XlsPnTOtNOz/Gv1s9dUxiJyOKSknoRqePJeRt9qyUJBh66fCRt0lNg5Wuwb5N/YkISnHhzlKIUEZGYZkw9XXDqtrY8fZA/qZ+9ulCnyzaQknoRcVmYt48HP1rnG990en8m9mkPHg98er978ogroE12hCMUEZEmo766eo/HdWlcr3a+02W3FZezbtfBSEUXV5TUi4hPcVklN7+QS43HWSUZ27MtM07v57y46jXYHXAioEmAk26LQpQiItJk9D4ZUgIOJTy4E3YscU1JTkzglAFZvvEcleA0iJJ6EQHAWsvPX1nGtmJnE1Nmi2QevnIUSYkJUFMFc/7gvmHoJdC+bxQiFRGRJiMpFfqe5r628vU609Ta8vgpqRcRAJ77agsfrPT/Iv2fS4fTrU0LZ7DkOXctvUmEU38Z4QhFRKRJGnShe7zi1TolOKfmZGGcw2VZtKWIotLKCAUXP5TUiwirtpfw+3f8pTXXTurJWUO8HW0qy2DeX903jL5Gq/QiInJ0cs52DimsVVIA+V+5prTPSGVktnMqucfCp+t1uuyxUlIv0syVVVZz0/OLqax2Vk0GdWnNL88Z5J+w4H/hwA7/OCkNJv88wlGKiEiTlZpRt2f98pfrTJsy0N0FR46NknqRZu7uN1ayaXcpAOkpiTx21SjSkhOdF8uL4PMH3TdM+LFz/LeIiMjRGnqpe7zyNWe/VoDTApL6T9YWUl3jLtGRw1NSL9KMvb5kGy8tKvCNf3/hUPpmBXQp+OIRqNjvH6dmwom3RDBCERGJC/3OgLQ2/nH5Ptj0iWvK4C6t6dw6DYCSimoWby2OYIBNn5J6kWZq0+6D/Oq15b7xxaO6ccmYgJP/DuyEr59033TSzZDeLkIRiohI3EhKgcEXuK8tf8k1NMa4D6JSF5xjoqRepBmqqKrhxv8uobSyBoDeHVryu4uGuid9eh9UlfnHLTvChOsjGKWIiMSVYdPd4zXvOM0YApyeE9DaUnX1x0RJvUgz9Pu3V7F6RwkAKYkJPHrlKDK8p/kBTvvKRU+7b5r8M0hpGbkgRUQkvvQ8ETI6+8eVB2Hd+64pJ/brQGqSk56uLzxI/j530i+hKakXaWbeWrqd/3y91Tf+zfmDGdot0z1p7p/AU+0ft+0Fo6+NTIAiIhKfEhKdgwsDrXjFNWyRksgJfdv7xjpd9ugpqRdpRvL2lPLLV/119OcO68K3J/RwT9qxtE6dI6f92qmHFBEROR7DgpL69R9CuXtDrPt0WSX1R0tJvUgz4dTRL+bgIWcFvke7dP58yTBM7RF+ANbCe79w39hpaN2VFRERkYboOhra9fGPayph9VuuKYGtLedv3EvpoWrkyJTUizQTf3p3NSu3++voH79qNK3Tkt2TVr4KW790XzvjHkjQrwoREQkDY+r2rA/6drh723RyOrUCoLLGw/yNeyMVXZOmv9QizcC7y3fwzPwtvvFd5wxkWPegOvrKMvjwt+5r/c+E/lMjEKGIiDQbw4KS+rzPnDbKAU4dmOX7ed663ZGIqslTUi8S57bsLeXnLy/zjacN6cy1J/SqO/GLmVDiP4iKhCQ468+NH6CIiDQvWTnQeZh/bD3OCbMBJg/wJ/WfrCvEWhup6JosJfUicayiqoYb/rOYA956xO5tW/DXS4e76+gBirfCFw+7r024Hjr0i1CkIiLSrAT3rF/+sms4tmc70lMSAcjfV07eXrW2PBIl9SJx7N63VtWpo89skVx34oe/geoK/7hlltOXXkREpDEMudg93rbQOSPFKyUpgRP6dvCN561VF5wjCVtSb4zpboz5pzFmuzHmkDEmzxgz0xjT9hje4xNjjD3MIy3EfYONMS8aYwqNMRXGmLXGmHuNMS3C9e8TaWpeW1LA8wv8/eh/fd4gRmS3qTtx82ew6nX3tSl3Q1pm3bkiIiLh0CYbekxyX1v2oms4OUd19cci6chTjswY0xf4EugIvAGsAcYDNwPTjDEnWmuPZevyvSGu1+lpZIyZAMwBkoGXgXzgdOC3wBRjzBRr7aFj+GyRJm/9rgPc9eoK3/jc4V24ZmLPuhNrquH9oBaWXUfByKsbOUIREWn2hl0KW+f7x4ufgZPvgEQnPT01oK5+/qa9VFTVkJacGOkom4ywJPXAEzgJ/Qxr7aO1F40xDwK3An8Erj/aN7PW3nM084wxicC/gHTgQmvtm97rCcCLwCXez//L0X62SFNXVlnNT/6zmPKqGgD6dGjJXy+pp44eYPHTsGuF+9rZ/6MWliIi0viGXgof/Bqqy51xyTbY8BHknA1Adrt0+mS1ZNPuUiqqPCzYvI9TAhJ9cTvuv9zGmD7AmUAe8HjQy3cDpcA1xpiWx/tZ9ZgMDAI+rU3oAay1HqC2IPh6U282IxJ/rLX86rUVbCg8CEBqUgKPXz2ajNR6/vu9bB/M+YP72rDLIHt8BCIVEZFmr0WbuocbLvyXaxjYBUclOIcXjuW4073PH3qTaR9r7QHgC5yV9IlH+4bGmMuNMb8wxtxmjDnbGJN6hM9+P/gFa+0mYB3QE+gT/LpIPHp+QT6vLdnmG//+oqEM6tK6/skf3wPlRf5xckuYGqryTUREpBGM/Z57vP5DpyObl5L6oxeOpD7H+7wuxOvrvc8DjuE9XwD+DDwAvAtsNcZcWs+8sH22MWZRfQ9g4DHELRI1K7bt5563VvrG08d057Kx2fVPzvscFv/bfe3k26B110aMUEREJEi30e6e9Vintt5rYp/2pCY56eqGwoMUFKm1ZSjhSOprW2TsD/F67fV62m7U8QZwPtAdaIGTUP/Ze+8sY8zZjfjZIk1WcVkl1z+3iMpq58uygZ1b8bsLh9Y/uaoC3rrZfa19f5h0UyNHKSIiEsSYuqv1i5+FmioA0pITmdCnve+lT9ftiWR0TUokdsPV1rMf8Sgwa+1D1tq3rbXbrLUV1tq11tq7gNtxYv1TI372mPoeOJ18RGKWx2O5dVYuBUXORqOM1CQev3o0LVJCdAj49D7Yu8F97YJHILnejrEiIiKNa9h0SMnwjw/uhLXv+YaBXXA+Ub/6kMKR1Neuhodqat06aF5DPIXTznKkMaZVhD9bJKY9PncDc9f66wzvnz6cvlkZ9U/etRK+mOm+NuY66HlCI0YoIiJyGKmtnPaWgRb5N8wG9qv/cuNe37fS4haOpH6t9zlU3Xp/73OouvcjstZWAAe8w8AuOo3+2SKx7NN1u3nwY///vH90Sh+mDe1S/2RPDbw5AzwBxz1kdNbmWBERib7gEpyNc2DfZsBpzdy9rXOe6MFD1SzeWhR8txCepH6u9/lMb394H++q+olAOfBVQz/AGJMDtMVJ7AOLqeZ4n6fVc08fnGR/C7Ap+HWRpm5bcTk3v7AE6y0uG9+7HT87Kyf0DQv+zzmGO9A59+nkWBERib4uI6DraPe1RU8DYMz/t3fn8VFV9//HXycbWUgIIYQdwr7vqwLK4r6LuOG+tHVpta22/VZtXartr7W1Lq1VqUgV1LoUrFpFK64ouwhlJxB2CBAIkJB1zu+POySZJJP1zkwmeT8fj3lc5tx7zv3M4zKZz5w551yjVXBqocFJvbU2A/gISAfurLD7YZye9ZettbknC40x/YwxPqvKGGN6GGM6VWzfGJOKc4MpgNetteXvKvs5sB44zRhzUbk6EcDvvU+fs9bWOKZeJJwUFJdwx5wVHM5zJhKlJbbgLzOGExXp5y19ZCd88ohvWb8LYMBFVR8vIiISbKNu8n2+ai4UFwIVlrbcqKS+Km7dUfYO4GvgaWPMVJxEeywwGWfoy/0Vjl/v3Za/KdRpwN+NMZ8DGUA20BU4D2fM/HLKbigFgLW2xBhzE06P/VvGmLeAHcBUYBTOGvl/duk1ijQav3lvHd/tcqaKREUY/nrNCNIS/Ux0tRbevweKcsvKWiQ5vfQiIiKNxaDLYMH9UHDUeZ57ADa8B4OmcWqvVKIjDUUllnV7j5J1NJ+0JC3wUJ4rq994e+tHAbNxkvl7gJ7A08Ap1tpDtWhmBTAHSAMu87ZxDrAGuAsYb609UsW5lwCjcZbDPAv4Cc6XgEeAM621BQ15bSKNzdsrdjFncdmNOX55Xn9Gp6f4r/C/t2HzAt+yMx7SmvQiItK4xCTAkCt9y5bPApyV3UZ1K/us0xCcytzqqcdauxO4qcYDnWNNFWVrgBvree51wOX1qSsSTv63O4f75q0pfX7+kA7cPD7df4Wje5xe+vK6nuKseCMiItLYjLoJls0se575JRzcDKm9Ob1vW77Z6vQTf77pAJf7u8FiMxWMdepFxAXZuYX84JUVFHiX8uqd1pLfXzYEYyp9R3Z4PDD/dsgv9wNXZAxc+BRE6K0vIiKNULuB0GWsb9myFwHfcfVfbj5IiUdTJsvTJ7tIGCgu8fCj11ay+4hzg6nEFlE8f91IWrao5se2pc/D1s98y6b+GtpWs0KOiIhIqFX8NXnly5CXTb/2ibRLagFAzokiVu2sNCq7WVNSLxIGHl+wkUVbyqam/PnKYfTwd4MpgKz18PGDvmXpE2FcxQWqREREGpmBl0JCWtnzolxY9iLGGE7rXdZb/9Xmg1VUbr6U1Is0cu+t3sPzX5TdauHuqb05Y0A7/xWKC+Ff34OScnPEW7SCS/6mYTciItL4RcfCuNt9y5Y8B4V5TOidWlr01RZNli1Pn/AijdjGfcf4+VurS59P7ZfG3VN7V1MD+PQx2LfGt+z8P0KyJhSJiEiYGHUzxCSWPc87CKvmMr5XWVL/7Y4jHC8orqJy86SkXqSRyjlRxA9eWU5eYQkA3VMTeOLKYURE+JkYC5C5CBY95Vs2cBoM1uJQIiISRuKSYfTNvmVfP01qXCQDOiQBUOyxLM6ozarpzYOSepFGqMRjufv1b8k8lAdAfEwkz183klZx0f4r5R+FebcB5VYDSOwIFzwB/lbIERERaazG3eGs2nbSkR2wbj4TfYbgaFz9SUrqRRqhPyzYwGflboP9+PSh9GmX6L/CybvG5uzwLb/0bxDXOkBRioiIBFBiexh6lW/ZV08yoVeb0qdfbta4+pOU1Is0Mu+s2s3zn5dNjL1zck/OH9Kh+krLZ8GaN3zLxt0BPSa5Hp+IiEjQnHo3UO7X5v1rGOv5lpgoJ4XNOJDL3pwToYmtkVFSL9KIrNmVU2li7D1n1rCu/O6V8OH/+ZalDYCpD1Z9vIiISLhI7QX9L/Qpiln8DGPSU0qff6mlLQEl9SKNRtaxfL7/yvLSO8b2SmvJk1fVMDE2LxveuAFKCsvKYlrCFS87S4KJiIiEuwk/9n2e+SXT0vaWPtV69Q4l9SKNQEFxCbfPWcnenHwAkmKjmHn9KBJjq5kY6/HA/Nsrj6O/6BlIrWHZSxERkXDRaSR0P82naGr2a6X/XrTlIB6PrVir2VFSLxJi1loefGctK7YfBiDCwDMzRtA9NaH6iouehE0f+paNvQ0GTQtQpCIiIiEy3re3PilzASPinUmyh3ILWb/vaCiialSU1IuE2CuLt/P6sp2lz395bn9O79O2mhrAti9h4W98yzqNgjN/U/XxIiIi4aznFGg/pPSpwfKzlmUdWxqCo6ReJKS+2HSAh99dV/p82vBO3Dqxe/WVju2Dt24G6ykri0uBy2dDVIzfaiIiImHLGBh/t0/R2KML6Gl2A1qvHpTUi4TMlqzj3PnqSkq84wCHdknmt9MGY6q7UVRxgTMxNjerXKGBaTMhuUtgAxYREQmlAZdAm16lTyPw8POofwKwdFs2+UUloYqsUVBSLxICh3MLueUfyziWXwxAh1axzLxuJLHRkf4rWQvv3g07F/uWn/5z6H1GAKMVERFpBCKjYOqvfYrOjlzOCLOJgmIPyzMPhyiwxkFJvUiQFRZ7uG3OCrYfygMgLjqSmdePIi2phiUov/ozfPeab1mPyXD6LwIUqYiISCPT/yJnNZxyfhH9OmD5ckvzvrusknqRILLW8ut3/seSbdmlZX++chiDOrWqvuL6d+GTh33LUnrC9FkQUU3vvoiISFNiDJzh+3k4NmIDUyK+bfaTZZXUiwTRi19t81np5mdn9+WcQe2rr7RnFfzr+75lsckw4w2IT6m6joiISFPVfSL0OtOn6OdR/2T9niMcOl4QoqBCT0m9SJAs3LCfx/6zvvT5tOGduGNSz+orHd0Lr10FRXllZRFRzh1jU3v5ryciItKUnfEgULawRL+InVwa8RWLMg6FLqYQU1IvEgRr9+Two1e/xXpveDeyW2t+d1kNK90U5jkJ/bG9vuXn/RF6nB64YEVERBq79oNhyJU+RT+NfpPFG3eFKKDQU1IvEmB7c05w8+xl5BY6S211So7j+etG0iKqmrHwnhKY9wPYu8q3fNwdMOqmAEYrIiISJibfB5Fl92fpZA7RfuNc7MketGZGSb1IAB0vKObm2cvZf9QZ45cYG8VLN40mtWUL/5WshffvgfX/9i3vfRac9WgAoxUREQkjrbvB6Ft9iq4rfovM3XtCFFBoKakXCZDiEg93zl3J+r1HAYiKMDx37Uj6tEusvuKnj8GKl3zL0gbAZS9qpRsREZHyJt4LMWWfq63NcY5/8scQBhQ6SupFAsBay4P/Xsvnm8rWzP3ttMGM75VafcVvnoUvHvctS+wIM/4JsUkBiFRERCSMJbSBCXf7FPXLfAUOZYQooNBRUi8SAC98sZW5S3aUPv/RlF5cMapL9ZW+ex0W/NK3LK41XDcPkrsGIEoREZEmYNwdFMenlT6NtkXY934CzWxsvZJ6EZf9Z81efvfBhtLnFw/ryE/P7FN9pU0LYP4dvmXRCXDNW5DWLwBRioiINBExCUSe7TvnzGz7HNa8GaKAQkNJvYiLlmVm8+N/lq1YMyY9hT9MH1L90pXbv4Y3rgdbUlYWEQ1XzYHOowIYrYiISNNghlzBxviRvoUL7oMTh0MTUAgoqRdxyeb9x7hl9jIKiz0AdE9NqHnpyl3L4dUroTi/XKGBy2ZCzymBDVhERKSpMIaMMY9QYKPLynIPwH8fCllIwaakXsQFe3NOcMOspRzNLwYgtWUL/nHTGFonxPivtHMpvHwJFBz1Lb/gCRh4aQCjFRERaXoGDxnBX4sv9i1cMRt2LAlJPMGmpF6kgXJOFHHjrGXsyXF62xNiIpl902i6ton3X2nHEnhlGhQe8y2f8gCMujmA0YqIiDRNXVLieS/pCjI8HXx3vPdjKCkKTVBBpKRepAHyi0r4/svL2bjfSc6jIgzPXTeSQZ1a+a+0/RuYU0VCf/ovnPV2RUREpF5G9+zAA8UVOsey1sE3fw1NQEGkpF6knjweyz1vfMeSbdmlZY9fPoSJvdv6r7T9a5hzGRQe9y2f9EvndtfVTagVERGRap3aqw3feAbydslE3x2f/T84vD00QQWJknqRerDW8pv31/H+mr2lZf93bj8uHd7Zf6XMr2DOdCjK9S2ffD9M+r8ARSoiItJ8nNKjDQCPFV3DYduybEfxCXj/nia9dr2SepF6+OunW3hpUWbp8xtPTecHp/XwX2HzxzD38soJ/ZQH4PSfByZIERGRZiYtKZZeaS3JJonfFV/tu3PLx7B8VmgCCwIl9SJ19Mo3mfzxo02lz88f3IFfXzDA/1r0q151lq0syvMtn/prOO1ngQtURESkGTq1p9Nb/2bJ6exMHOa7c8F9kLWhilrhT0m9SB28s2o3v/732tLnE3ql8sSVQ4mIqCKhtxa+ehLm3+57YymAMx6CifcENFYREZHm6GRSb4ngt9E/gpjyw3Dy4e1boSjfT+3wpaRepJYWbtjPPW98Vzocb1iXZP83l/J4nN6A/z5YYYeB8/4IE34S8HhFRESao7Hd25SuO/HRvnhOnPl73wP2r4FPHg5+YAHmWlJvjOlsjJlljNljjCkwxmQaY540xrSuZf0EY8w1xphXjTEbjDG5xphjxpjlxph7jDFV3sXHGGOreSx26/VJ87Z0Wza3z1lJscfJ6Pu2S2T2TaNJaBFV+eDiQvjX92Dxs77lkTFw+WwY873ABywiItJMtU6IYUCHJABKPJZvWp4Bg6b7HrT4Wdj83xBEFzhVZCR1Z4zpCXwNpAHvABuAMcDdwDnGmPHW2kM1NDMRmANkA58C84EU4ELgj8A0Y8xUa21Vv5dsB2ZXUb6r7q9GxNf/dudwy+xlFBR7AOiSEsfLt4whOb6K75n5OfDG9bD1M9/yFklw1avQfWLlOiIiIuKqU3u2Ye0e547tX2dkM+WCJ2DXUjiyo+yg+bfB7V9Dy7QQRekuV5J64FmchP4ua+0zJwuNMU8APwEeA26roY19wLXAm9bawnJtJAKfAacCdwJ/qqJuprX2oQbEL1KlLVnHuWHWUo4VFAPQNrEFc24ZS7uk2MoHH8qA166Cg5t8y1u2g2vfhvaDgxCxiIiInNozlZlfbgPg64xDcMEAmDYTXjoXrNNJR+4BmH8HXPNmk7hPTIOH3xhjegBnAZlAxdt1PQjkAtcZYxKqa8dau8paO7d8Qu8tP0ZZIj+pofGK1FbmwVxmzFzMoVznv2RSbBSv3DKGbm2q+K+89TOYOaVyQp/SE275SAm9iIhIEI3unkKkdxGLdXuPcji3ELqOc+7eXt6Wj2HJ8yGI0H1ujKmf4t1+ZO3Jrz4Ob0K+CIgHxjXgHEXebbGf/cnGmJuNMfcZY+40xjTkXCLszM5jxszFZB0rACA+JpKXbhpDv/ZJvgdaC0tegFemQf4R332dRjkJfev04AQtIiIiALRsEcXQzq1Kny/e6h0FPvFe6FIhTfz4V7BzaRCjCww3kvq+3u0mP/s3e7d9GnCOm73bD/3sHwq8iDPM5y/AN8aYVcaYWnePGmNWVPUA+jUgbglDe3NOMOPvi9mT40zfiI2OYNaNoxnZrcKc7+JCeO/H8MHPKi9ZOfgKuPE9SEgNUtQiIiJS3qk9yz6Dv87wJvWRUTDtBWeu20klhfD6NZAT3lMx3UjqT34NyvGz/2R5cn0aN8b8EDgHWAVUdRuwJ4DxQFsgERgNvIWT6C80xnSqz3mleco6ms+MmUvYmX0CgJioCGZeP4px3ttOlzp+AF65FFbMrtCCgTMedv5gRMcFJWYRERGp7OR69QBfZxws29G6G1z4lO/BuVnw2tVQWOHO72EkGOvUn5x5YOtc0ZhpwJM4k2gvs9YWVTzGWnuPtfZra+1Ba+1xa+1ya+3lwNtAKnBvbc5lrR1Z1QNnJR9pBg4dL+Cavy9h20HnDR0daXju2hFM7N3W98BtX8JzE2D7V77lMS3h6tdhwo+bxIQbERGRcDaiW2tiopxUN+NALvuPlltAcdA0mPBT3wr7Vjs3jPR4CEduJPUne+Jb+dmfVOG4WjHGXAK8DmQBk6y1W+sY13Pe7Wl1rCfN0JG8Qq59cSmbs44DEBlheObqEUzp167sII8HPn8cXr4Iju/zbaB1Otz6X+h7TvCCFhEREb9ioyMZ2bVs6Ow3GRVWV5/yK+h7vm/Zunfgiz8EITr3uZHUb/Ru/Y2Z7+3d+htzX4kx5nLgTWA/cLq1dmMNVapywLutdtUdkezcQq6euYT1e531bCMMPHnlMM4Z1L7soOMHYO5l8OmjZUthnZQ+Eb73KaT1D2LUIiIiUpPyQ3AWbTnouzMiAqY9D2kDfcs/+x2snReE6NzlRlL/qXd7ljHGpz3vGvPjgRNAre7uaoyZAbwG7MFJ6DfXUMWfk1Ob69rDL83IweMFzJi5uDShNwb+MH0oFw7tWHZQ5iJ4fiJkLKxQ2ziz6K+bD/EpwQtaREREauWUckn9km3ZlQ9okQhXvwbxFebOzbsd9qwKcHTuanBSb63NAD4C0nFuDlXewzg95S9ba0tnHhhj+hljKq0qY4y5AXgF2AGcVtOQG2PMiKrWvzfGDMFZCQecu9SKVHLgWAFXv7CYDfuOAU5C//j0oUwf2dk5oKQIFj4G/7gAju31rRzfBq59C6b+yplJLyIiIo3OkM7JxEY76e6O7Dz25pyofFDrbnDlHIiILisrPgGvz4Bj+yof30i5lY3cAXwNPG2MmQqsB8YCk3GG3dxf4fj13m3pbEJjzGSc1W0icHr/bzKVJxsesdY+We75XcA0Y8xCYCdQgLME5TlAJDATp9dfxEfW0XyunrmYjAPOd80IA09cMYxLhnsXS8paD/N+AHu/q1y566kw/UVI6lh5n4iIiDQaMVERjOzWmkVbnPH0S7Zml33Wl9ftVLjgCfj3j8rKju52lrq88X2IruJO8o2MK0m9tTbDGDMKeAQnoT4P2As8DTxsra3i945KulH2y8HNfo7ZjrMazknzcSbiDsG5CVYscAj4AJhprf13HV+KNAP7cvKZMXMxW72r3ERGGJ68cpgz5MZTAoufhU9+AyUFlStPvAcm3afeeRERkTAxtnubsqR+26Gqk3qAEdc7nXqLny0rS+5KPRZwDAnXMhNr7U7gploeW6kL3lo7G5hdx3POx0nsRWplz5ETXD1zMdsP5QEQFWF4+urhnDe4AxzOhPl3wPZFlSu2bAcXPwu9zwhuwCIiItIgY7uXzXtbvLWGfuYzfwMHNkLGJzD5ATjt3rBZplrdjdJsbD1wnOteXMruI854uqgIw19mjOCcAWmw7O/w8YNQeLxyxQGXJMO1PQAAGJVJREFUwAV/1mRYERGRMDS0SzItoiIoKPaw7WAuWUfzSUvyM5wmMgqmz4KdS6DP2cENtIGCcfMpkZBbuyeHK57/pjShj440/O3akZyTehBmnQXv31M5oY9NhstehMtnK6EXEREJU7HRkQzvmlz6fHFVq+CUF5ccdgk9KKmXZmBZZjZXvbCYg8cLAYiLjuSlawZx5u5n4YXTYdeyypV6ToU7voHB08PmZzcRERGp2tjuZUtWLt56qJojw5eG30iT9tnGLG6bs4L8IueGUUmxUbx9Zh69PzofjuyoXCGmJZz5CIy6Wcm8iIhIEzGuRxue+sS59dESJfUi4eXd7/bw0zdWUVTizFofknCEOV3fI+nj/1Rdod8FcO7voVXnIEYpIiIigTa8azIxkREUlnjIOJDLgWMFtE1sEeqwXKXhN9IkzV2ynbte/5aiEktL8vhNwpu8Y39M0rYqEvqkTnDlXLhqrhJ6ERGRJig2OpJhXcrG1S/Z1vR665XUS5NireXxBRu4f97/MNbDFZGf8kXcvVxXMg/jKfQ92ETAuDvgziXQ/4LQBCwiIiJBMbZH2aIXS2pa2jIMafiNNBmFxR5+8fZq5n27m1Mi1vJA1BwGRmyv+p4RHUc4d47rODzocYqIiEjwjevRhmcWbgGaZk+9knppEo7mF3H7nBXkZSxmbvQbjI9cW/WBiR3gjIdg8BUQoR+qREREmosRXVsTHWkoKrFs2n+cQ8cLaNOy6YyrV1IvYW9vzgke+fsb3HTkJc5o8W3VB0XFwvi7nUdMQnADFBERkZCLi4lkSOdkVmw/DMDSbdmcO7hDiKNyj5J6CWtbN3xLxhv38zfPIoj0c9Dgy2Hqg5DcJaixiYiISOMyrkdKaVK/REm9SCOwZxX7//M70ncuoIepatA80GMSTPkVdB4VzMhERESkkRrbvQ1//TQDaHo3oVJSL+HDWtj+NfbLP2EyPqEdQFX3h+o8Bqb+CrqfFuQARUREpDEb2a01kRGGEo9lw75jHM4tpHVCTKjDcoWSemn8PB7YvAC++jPsXFJlHg9A+8FOz3zvs3Q3WBEREakkoUUUgzu1YtXOIwAszczm7IHtQxyVO5TUS+OVfxRWvQpLn4fsrX4PK247kKhJP4P+F2tFGxEREanWuB5tSpP6JVuV1IsETvZWWPICfDsHCo/5PSwzfjCdLnqA6L5nq2deREREamVsjxSe+7zpjatXUi+NQ0kxbPkYVsyGTQuo+o5Rjs89Q8kdczfnnj8No2ReRERE6mBUt9ZEGPBYWL/vKDl5RbSKjw51WA2mpF5C6/B2+PYV+HYuHNvj97BCG8m7nlP4Z+SF3HXddM7rnRrEIEVERKSpSIyNZnCnVny3KwdrYVlmNmcMaBfqsBpMSb0EX3EBbPoQVvwDMhZSXa/8AZvE3JIzmFt8Bm3ad+Fv146ke6puHiUiIiL1N7ZHG77blQPAkm2HlNSL1JrHAzsXw+p/wtp5kJ9T7eFrbXdeLDqb9zynUEg0l43ozKOXDCIuxt8dpkRERERqZ2z3FF74wlmEY8m27BBH4w4l9RJYBzY5ifyaN+DIjmoPtdEJrGo1hYd3j2aV7QkYYqIi+H8XDeTK0V00fl5ERERcMSo9BWOcW+Cs3XOU3IJiElqEd1oc3tFL43RgI6x7B9bOh6y1NR/fcTj7e1/JHd/1YMWu4tLiLilx/O2akQzq1CqAwYqIiEhz0youmr7tEtmw7xglHsvKHYeZ2LttqMNqECX10nDWQtY6J5Ff9w4c2FBznfg2MHAadvi1vJyZzG//s56C4rKE/oz+7fjT5UObxGx0ERERaXzGdE9hwz5n6exlmUrqpbkqLoTti5wJrxs/gCPba64TFQt9z4MhV0KvqWTllfDzt1bz2cay3vyYqAh+eW4/bjglnYgIDbcRERGRwBiVnsLL3zj5y7ImMK5eSb3U3vEs2PIJbPoAtiys9sZQpUwEpE90Evn+F0JsEgAfr9vPL95eTXZuYemh/don8tRVw+nbPjFQr0BEREQEgDHpKaX//nbnYQqLPcREhe+d6ZXUi39F+c6KNRkLnce+NbWrFxEF3U+HARdDv/MhoWxN+ezcQh55dy3zV/muSf+9id259+y+tIjS6jYiIiISeO1bxdIlJY6d2SfIL/Lwvz05jOjaOtRh1ZuSeilTUgz7VkPmV7Dtc8hcBMUnalc3sgX08Cbyfc+D+BSf3dZa/v3dHh5+d51P73z7pFj+dMVQxvfSzaREREQkuEanp7AzezfgDMFRUi/hqXwSn/kV7PgGCo7Wvn5CGvQ5G/qcAz0mQYuWVR62+8gJHpi3hk83HvApv3hYRx66cCCtE2Lq/xpERERE6ml0egr/WulN6jMP84PTQxxQAyipb05OHIFdy2HnEuexewUUHq9DAwY6DodeU6HPuc6/I/yPPSvxWOYu2c7vP9hAbmFJaXnHVrE8eukgpvQL/7u3iYiISPgaXW5c/fLt2Xg8NmwX6lBS31SVFEHWetizEnavhF3LnOfYurWT1Al6ToaeU53e+ArDavxZsvUQD7+7jnV7y3r+jYHrx3XjZ+f0o2WY3+BBREREwl/PtgmkJMSQnVvIkbwithw4Tp924blghzKrpqCkGA5thr2ry5L4fauhOL/ubcW3gW7jIX2Ck8Sn9nGy8VradTiP332wgfdX7/Up79k2gT9MH8LIbrX7UiAiIiISaMYYRnVrzUfr9gOwdFu2knoJkvyjTo/7vtXOajT7VsP+dVBSUL/24lMhfbyz7GT6BEjtW+2QGn/yCot57vOtPP95BgXFntLy2OgIbj+9F7dN6qGVbURERKTRGdM9pTSpX56ZzbXjuoU4ovpRUt9YFeXDwY1OAp+1zrtdDzk7G9CogbT+0GWs9zEGUnrUqSe+UpglHv61chdP/ncze3N8fxm4aGhH/u/cfnRMjmtAzCIiIiKBU35c/bLMwyGMpGGU1DdGX/4JFj4K1lPzsdVp2R46jYCOI6DTcOg0CuKSXQmxuMTDO6v28PTCzWw/lOezb1CnJB68cKDPm0RERESkMRrYMYn4mEjyCkvYfeQEu4+coFMYdkgqqW+MWrave0Lfsh20HwLtB0OnkU4yn9TR9dBKPJb3Vu/hqf9uZuvBXJ99qS1j+PnZ/Zg+snPYzhwXERGR5iUqMoLhXZNZtOUQ4KxX32l4pxBHVXdK6hujtP7+95lIaNML2g3wJvHeRD4xsMtDFhZ7eG/1Hv72WQabs3yXwWwVF833T+vBjaemk6BVbURERCTMjE5PKUvqM7O5REm9uKJtPzAR0KozpA1wkvy0gc42tTdEtQhaKIeOFzB3yQ5eWbydA8d8J+MmxkZx64Qe3DwhncTY6KDFJCIiIuKmMT7j6rNDGEn9KalvjGLi4Ze7ICYhZCFs2HeUl77KZN6q3RQW+w4FSoiJ5OYJ3bl1Qg9axSuZFxERkfA2rGsyURGGYo9l0/7jHM4tDLs73iupb6xCkNDn5BXx/pq9/GvlLpZvrzz7Oy2xBTecms6MMV3D7j+6iIiIiD/xMVEM7NSK73YeAWD59sOcOSCwQ5vdpqS+mSss9vDZxizmfbubT9ZnUVhSeYLukM6tuGVCd84d1IGYqLqvYS8iIiLS2I1Jb12W1GdmN9+k3hjTGXgEOAdoA+wF5gMPW2trveinMSYF+DVwCdABOAR8CPzaWrsrkOduLo4XFPPV5oN8tjGLBWv3cTivqNIxkRGGswa045YJ3RnZrTWmAWvZi4iIiDR2o9NTmPnlNgCWhuG4eleSemNMT+BrIA14B9gAjAHuBs4xxoy31h6qRTttvO30ARYCrwP9gJuA840xp1hrtwbi3E2ZtZYtWcf5bOMBPt2YxbLMbIpKbJXHDu7UikuHd+KiYR1JbRm8CbkiIiIioTSq3GTZNbtyOFFYQlxMZAgjqhu3euqfxUmq77LWPnOy0BjzBPAT4DHgtlq081uchP7P1tqflmvnLuAp73nOCdC5m4ycvCJW7z7CdzuP8N2uHL7beYSsCivXlNexVSyXDO/EtBGd6JWWGMRIRURERBqHlIQYeqW1ZEvWcYo9lm93HubUnqmhDqvWjLVV99jWugFjegAZQCbQ09qyuyYZYxJxhsIYIM1am1tlI86xCcABwAN0sNYeK7cvwnuOdO85trp57hpe34oRI0aMWLFiRX2qB0x+UQm7Dp9g5+E8dh0+wa7sPHYezmP93mNsO1jzSx3QIYnJ/doyqW8aI7u21s2iREREpNn75b/W8NrSHQD89Mw+3DW1d1DPP3LkSFauXLnSWjuyrnXd6Kmf4t1+VD6pBrDWHjPGLALOAsYBn1TTzilAnLedY+V3WGs9xpiPgO8Dk4GTQ3DcOnej84cPN7D9UB55hcXkFZZwoqjE2RaWkFtYzJEqxsFXJ7FFFBN6pzK5bxqn921Lu6TYAEUuIiIiEp7GdG9dmtSH23r1biT1fb3bTX72b8ZJrPtQfWJdm3bwtuP2uTHG+OuK71ddvUD5bOMB1u09Wq+60ZGGfu2TGNqlFUM6JzOsSzI927YkUr3xIiIiIn6N6lY2rn7l9sMUl3iIigyPlf/cSOpbebc5fvafLE8OQDtunbvRia9hYkZkhKFjciydk+PpkhJH59bONr1NAv07JBEbHT4TO0REREQag86t4+jQKpa9OfmkJrZg39F8OreOD3VYtRKMdepPdg83bPB+/dqpdR1/Y5e8Pfgj6nBOV/xwSi+O5heTEBNJXEwk8TFRxMdEEhcdSXxMJK3iosPmm6OIiIhIODDG8Ow1I+iUHEdamA1VdiOpP9kb3srP/qQKx7nZjlvnbnQm9U0LdQgiIiIizc7wrq1DHUK9uNHVu9G77eNn/8lpw/7GvTekHbfOLSIiIiISttxI6j/1bs/yLj1Zyrus5HjgBLC4hnYWe48b761Xvp0InAmv5c/n5rlFRERERMJWg5N6a20G8BHOGvJ3Vtj9MJAAvFx+nXhjTD9jjM+qMtba48Ar3uMfqtDOD73tLyh/R9n6nFtEREREpKlxa6LsHcDXwNPGmKnAemAszprym4D7Kxy/3rutuMbifcAk4KfGmGHAUqA/cDGQReXEvT7nFhERERFpUlxZPsXbYz4KmI2TUN8D9ASeBk6x1h6qZTuHcG5C9TTQy9vOWOAlYKT3PAE5t4iIiIhIuHJtSUtr7U7gploe6/cuSNbabOBu78P1c4uIiIiINDVa6FxEREREJMwpqRcRERERCXNK6kVEREREwpySehERERGRMKekXkREREQkzCmpFxEREREJc0rqRURERETCnJJ6EREREZEwp6ReRERERCTMKakXEREREQlzxlob6hgaNWPMobi4uJT+/fuHOhQRERERacLWr1/PiRMnsq21bepaV0l9DYwx24AkIDMEp+/n3W4IwbklOHSNmwdd5+ZB17l50HVu+kJ5jdOBo9ba7nWtqKS+ETPGrACw1o4MdSwSGLrGzYOuc/Og69w86Do3feF6jTWmXkREREQkzCmpFxEREREJc0rqRURERETCnJJ6EREREZEwp6ReRERERCTMafUbEREREZEwp556EREREZEwp6ReRERERCTMKakXEREREQlzSupFRERERMKcknoRERERkTCnpF5EREREJMwpqRcRERERCXNK6oPIGNPZGDPLGLPHGFNgjMk0xjxpjGldx3ZSvPUyve3s8bbbOVCxS+019DobYxKMMdcYY141xmwwxuQaY44ZY5YbY+4xxsQE+jVIzdx6P1do8zRjTIkxxhpjHnUzXqk7N6+xMWawMeZlY8xOb1tZxpjPjTHXByJ2qT0XP5snGGPe8dbPN8bsMMb8xxhzTqBil9oxxkw3xjxjjPnSGHPU+zd2Tj3bcv1vv1t086kgMcb0BL4G0oB3gA3AGGAysBEYb609VIt22njb6QMsBJYB/YCLgSzgFGvt1kC8BqmZG9fZ+wHwAZANfApsAVKAC4H23vanWmvzA/QypAZuvZ8rtJkIrAZSgZbAY9baB9yMW2rPzWtsjLkR+DuQB7wHZALJwCBgj7X2KpfDl1py8bP5duBZIBeYB+wCOgPTgHjgAWvtY4F4DVIzY8wqYChwHOfa9APmWmuvrWM7rv/td5W1Vo8gPIAFgAV+VKH8CW/5c7Vs53nv8U9UKL/LW/5hqF9rc364cZ2BYcA1QEyF8kRghbede0L9Wpvzw633c4W6s3C+yN3nbePRUL/O5vxw8W/2OKAYWAW0r2J/dKhfa3N+uPQ3Oxo4ApwA+lbY1x/Ix/lC1yLUr7e5PnCS7t6AASZ5r+2cUPx/CeRDPfVBYIzpAWTg9M70tNZ6yu1LBPbi/EdLs9bmVtNOAnAA8AAdrLXHyu2L8J4j3XsO9dYHmVvXuYZzzADmAu9Zay9scNBSZ4G4zsaYi4H5wHVAFPAS6qkPGTevsTHmC2AiMNha+7+ABS115uJncztgH7DaWju0iv2rgcFAqg1lL64AYIyZhPMreJ166oPxGd9QGlMfHFO824/K/ycA8Cbmi3B+nhtXQzunAHHAovIJvbcdD/CR9+nkBkcs9eHWda5OkXdb3IA2pGFcvc7GmDRgJjDfWluvMZ7iOleusXee00RgObDWGDPZGHOvd27MVG9njISOW+/lLJwOtz7GmN7ldxhj+uD0EK9SQh/2gvEZ3yD6gxIcfb3bTX72b/Zu+wSpHQmMYFyfm73bDxvQhjSM29f5BZy/xbc1JChxlVvXeHS54xd6H48DfwT+C6wyxvRqQJzSMK5cZ+sMebgT5328whjzD2PM74wxL+MMmVwLXO5CvBJajT4HiwrViZuZVt5tjp/9J8uTg9SOBEZAr48x5ofAOThjc2fVpw1xhWvX2RhzM84k9yuttftdiE3c4dY1TvNurwAO4kya/ARoCzyIM9zqfWPMYGttYf3DlXpy7b1srX3TGLMHeA0ov6LRfpzhdBoSG/4afQ6mnvrGwXi3DZ3g4FY7Ehj1vj7GmGnAkzjjNi+z1hbVUEVCp1bX2RiTjnNN37TWvhHgmMRdtX0vR5bb3mqtnWetPWqtzQBuwBmW0we4LDBhSgPV+m+2MeZanF9fvsSZHBvv3X4C/AV4PUAxSuMR8hxMSX1wnPz21srP/qQKxwW6HQmMgFwfY8wlOB8IWcAkTYIOObeu8yyc1TLucCMocZVb1/iwd1sA/Kf8Du+QjXe8T8fUNUBxhSvX2TtufhbOMJvrrLUbrLUnrLUbcH6NWQFc7p2gKeGr0edgSuqDY6N362+c1cmJNf7GabndjgSG69fHGHM58CbOT7inW2s31lBFAs+t6zwCZ3jGAe+NUKwxxuL8VA9wv7dsfsPClXpw+2/2sYoT67xOJv1xdYhN3OPWdT4LZ1nLz6uYQOkBvvA+HVmfIKXRaPQ5mMbUB8en3u1ZxpiIKpZBGo/TY7e4hnYWe48bb4xJrGJJy7MqnE+Cy63rfLLODOBlYDcwWT30jYZb1/llnJ/oK+oNnIYzd2IF8G2DI5a6cusar8YZS59qjGlXxbyJQd5tZsNDlnpw6zq38G7b+tl/slzzJsKbq5/xgaCe+iDwjp/8CGcN+Tsr7H4YSABeLr+uqTGmnzGmX4V2jgOveI9/qEI7P/S2v0DJX2i4dZ295TfgXOsdwGm6po2Hi+/nu6y1t1Z8UNZT/7637K8BezFSJRevcTHODQMB/lB+CUtjzGDgRpzlad9y+SVILbj4N/tL73a6MWZI+R3GmGHAdJxx1gvdi14CxRgT7b3OPcuX1+f/S7Dp5lNBUsWthdcDY3HWlN8EnFp+DVvvz/BYa02Fdtp42+mD8wdiKc5knItxxlyf6v2PJyHgxnU2xkzGmXAVgTNOc2cVpzpirX0yQC9DauDW+9lP2zeim0+FnIt/s+NxJkuOw/nV5TOcntvLcIbd3GOtfSLAL0f8cPE6zwJuwumNnwdsx0n+LgFigCettT8J8MsRP7xz0y7xPm0PnI2zItHJL2QHrbX3eo9NB7YB26216RXaqdP/l6Bz69a0etTq9sJdcD6s9+K88bcDTwEpVRxr8c6lqmJfirfedm87e3GSv86hfo16NPw64/Te2RoemaF+nc394db7uYpjT17/R0P9Gpv7w8W/2fE4v65uwJk0m4Pzxf3cUL9GPdy5zjgrn9yI86XtMM4vMNk4X+iuCvVrbO4P7/uvVp+pOF/G/H7O1uX/S7Af6qkXEREREQlzGlMvIiIiIhLmlNSLiIiIiIQ5JfUiIiIiImFOSb2IiIiISJhTUi8iIiIiEuaU1IuIiIiIhDkl9SIiIiIiYU5JvYiIiIhImFNSLyIiIiIS5pTUi4iIiIiEOSX1IiIiIiJhTkm9iIiIiEiYU1IvIiIiIhLmlNSLiIiIiIQ5JfUiIiIiImFOSb2IiIiISJhTUi8iIiIiEub+P4ChKARwoCecAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 265,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xrange, p.pdf(xrange), label=\"$p(z)$\")\n",
    "plt.plot(xrange, q_dist(xrange), linewidth=2, label=\"$q(z)$\")\n",
    "plt.legend(fontsize=12)\n",
    "plt.title(\"Normalized sampling distribution\", fontsize=15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 26s, sys: 1.01 s, total: 1min 27s\n",
      "Wall time: 1min 26s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "zrange = np.linspace(0, 1, 50)\n",
    "empirical_cdf = np.empty_like(zrange)\n",
    "\n",
    "for ix, zval in enumerate(zrange):\n",
    "    qi = quad(q_dist, 0, zval)[0]\n",
    "    empirical_cdf[ix] = qi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dOnRgzJgxfPnllwAsXryYdu3a0blzZ5cjE6lg1sKGz2HWk3Bka5FNS3xJ/E/urfia9+E3l3amf0LV+wBG5HwpQRMRkSrh+++/5+DBg4BTFfHKK68M6aIg5ZGSksK2bdvYsGEDAJ9++inNmjWjXr16LkcmUkHS98Dnj8DGL4p0b/c14U/em1hUYxC/vrwL1/VpiccTehVZRSpD1f7LJiIi1cLOnTuZP39+oD169GgaNGjgYkTBYYzhyiuvpG7dugBkZWXx0UcfkZeX53JkIkHm88HSKfDP/kWSs+M2lt/n3sronL9Qr8+1fPvohVzfr5WSM6nWlKCJiEhIK35pY7t27ejTp4/LUQVPTEwM1157bWD9tp07d/L999+7G5RIMB1OhTcuhxm/hOyCiqVve0cyPPs55je+kXfvHc6fru1B/bhoFwMVCQ26xFFERELat99+y+HDhwGIjo4Oi0sbi2vdujUjRozgm2++AWDOnDm0bduWxMRElyMTOQ++PJj/Inz/R/BmBbq3+ZrwWO5d/BTVjYcuTWLioLZERoTX77TI+dBvg4iIhKzdu3ezYMGCQHvMmDFhe3/W4MGDSUhICLQ//vhjTp486WJEIuchfS+8eSXMfiqQnHmth//1Xs7YnD8T3X4oXz80jDuHJig5EylGvxEiIhKSrLXMmjUr0E5MTKR3794uRlSxPB4PV199NXFxTjnxjIwMpk+fHri0U6TK2PINvDIEthcsibHW14Yrc37PyxHjefqaPrx5ewot68e6GKRI6FKCJiIiISk1NZXt27cDTjGNiy++OHCfVriqXbs211xzTaCdmprKtm3bXIxI5CzkeeGbZ7BvXQunDgHgs4bnvddwZc7vaZSUwsyHh3FjSuuw/10WOR+6B01EREKOz+dj9uzZgXbv3r2Jj493MaLKk5iYyMCBAwOXdq5YsYLmzZu7HJVIGY7vho/ugLQFgQWnD9h6PJj7c9ZGJ/Onq7tybe8WSsxEykEzaCIiEnLWrl3Lvn37AIiMjGT48OEuR1S5LrzwwkDp/ZycHFasWOFyRCJnkPot9pUhkFZwv+icvG5ckv1HbNuhfPXLYVzXp6WSM5FyUoImIiIhxev18u233wbaAwYMoE6dOi5GVPmio6O59NJLA+3t27ezdetWFyMSKYG1sOCf2LeuxWQeASDPGv5f7vXc6fs1P7u4P+/cOYDm9WJcDlSkalGCJiIiIWX58uUcPXoUgJo1azJ48GCXI3JHUlISXbt2DbRnzJhBbm6uixGJFJKbBZ/cB18/jrE+APbbetyU8xu+anALH903lLuHJ2rBaZFzoARNRERCRnZ2Nj/88EOgPXToUGJiqu+n72PHjiUqKgqAI0eOMGfOnDKOEKkEJ/Zhp14Kq94JdC33teey7D/Qsf9YZvxiKN1a1HUxQJGqTQmaiIiEjIULF5KRkQFAnTp1SElJcTkid9WuXZvk5ORAe+7cuRw4cMDFiKTa27UM37+GY3YvDXR94B3GXZ5nePa2Ufz+qm7EREe4GKBI1acETUREQkJGRgbz5s0LtC+44ILA7FF11r59+0AFS5/Px4wZM/D5fC5HJdXSqvfxTRmL56RTwCfPGp7JHc/bTX/FJw9eyKguTVwOUCQ8KEETEZGQMGfOHHJycgCIj48vMnNUnRlj6NevHx6P8yc7LS1NVR2lcvnysDOfhOl34clzfkeP2Thuy30Mz8D7+Pc9g7TotEgQKUETERHXHTt2jCVLlgTaI0eOJCJCl0nlq1evHoMGDQq0Z82aFbgUVKRCZR0n7+0bMPNfCHRt8rXgFvNHJtwykd9c1oXoSL2dFAkm/UaJiIjr5s2bR15eHgAtW7akU6dOLkcUeoYNG0b9+vUByMrKKlJMRaRCHE4l918jiUidFeialdeb3zZ6nlceGMfork1dDE4kfClBExERV506dYqVK1cG2hdeeKEWtC1BdHQ0Y8aMCbSXLl3KoUOHXIxIwlrqd+T+60Kijm4OdL3svYLvej7HG/eOoFUDXdIoUlGUoImIiKuWL18eWN+rSZMmJCQkuBxR6OrYsSNt2rQBnIIh33zzjcsRSdixFt/CV/BNu5aonOMAZNsoHvHeT4Mr/sCz1/akRqQuPxapSErQRETENXl5eSxatCjQHjBggGbPzsAYw+jRowPt9evXk5aW5mJEEla8OeR++iCer36FB+eS4/22HvdG/w/j7/4vbkxp7XKAItWDEjQREXHNunXrOHHiBABxcXF0797d5YhCX4sWLejWrVugPXPmTKy1LkYkYSHjMNlTriBq5RuBrpW+BJ5q8k/+8uAkeraq52JwItWLEjQREXGFtZYFCxYE2v369SMyMtLFiKqOwlUud+3axbp161yOSKq0A+vJ/t/h1Nhd8Pv4Sd4gPu/zOi/efQnxtWq4GJxI9aMETUREXJGWlsaePXsAiIiIoG/fvi5HVHXUr1+flJSUQHv27Nl4vV4XI5Iqa+NX5P7fSGqc3Bno+mveDWRf/gpPXNmbqAi9VRSpbPqtExERVyxcuDDwvEePHtSqVcvFaKqeoUOHUrNmTQCOHj3K0qVLXY5IqhRr8c19AfvujUR5nTX1MmwNHjL/xdBJf+SGlDYuByhSfSlBExGRSnf06FE2bNgQaA8YMMDFaKqm2NhYhg0bFmj/8MMPZGZmuhiRVBnebLzT78Uz+0kMzv2Lu2w8D9f6Cw/d/zD9Exq6HKBI9aYETUREKt2iRYsChS0SEhJo0qSJyxFVTSkpKdSr5xRvyMzMZO7cuS5HJCEv4xA5Uy4ncvW7ga6lviT+0upl/vqLW2jdUOubibhNCZqIiFSqrKwsli9fHmgPHDjQxWiqtsjISEaOHBloL1y4kGPHjrkYkYS0/evIfeUConcXLG3xYd4wZvV9leduH03tmlEuBici+ZSgiYhIpVqxYgU5OTkAxMfHk5iY6HJEVVvXrl1p3rw54KwrN2fOHJcjkpC0aSbe10YRdcIpBuKzhj95byLzkhf59RU9ifBo/UGRUKEETUREKk1JC1N7PPpTdD48Hg8XXXRRoL1ixQrNokkBa2HBP7Hv3EBk7knAKQbyC/so/W99hvED27obn4icRn8VRUSk0mzYsCGQPMTExNCjRw+XIwoP7dq1o1WrVgD4fD7diyaOvFzsZw/C149j8AFOMZCfRT3LvXf/ggs7NXY5QBEpiRI0ERGpNIVLwfft25fo6GgXowkfxhguuOCCQHvFihUcP37cvYDEfaeO4Jt2DWb5G4GuZb4OPFLn7/z1/lvo1qKui8FJVWWMaWmMmWyM2WOMyTbGbDfG/MMYU/8sx2ngP267f5w9/nFblnHcUGPMR8aYvf7j9hpjZhpjLjm/7yy0KEETEZFKcezYMbZt2wY4CYUWpg6uhIQEWrZ03tvk5eVpFq06O7QF32sX4dn+Y6Bret5g/tn6OV79+SU0rxfjYnBSVRljEoFlwCRgMfAcsBV4EFhgjCnX+gz+/Rb4j0v1j7PYP+4yY0xCKcf9BvgRGAZ8BfwN+AyoD1xwrt9XKIp0OwAREakeVq1aFXiekJBA3br6BD+YjDEMHz6ct99+G4Dly5czdOhQ6tSp43JkUqm2/oDv37fhySq4D/GvuePY0/3n/GtcMlER+mxeztnLQGPgAWvti/mdxpi/Aw8BfwDuKcc4zwJJwHPW2ocLjfMA8Lz/PGMLH2CMGQf8HpgNXGOtPVFse1iVINVvqYiIVDhrLStXrgy0e/bs6WI04at9+/a0aNECcGbR5s2b53JEUqmWvYF965pAcpZlo7gv5wFyBz/CX6/vqeRMzpl/Vms0sB34Z7HNTwEZwHhjTFwZ48QB4/37P1Vs80v+8ccUnkUzxniAPwOngJuLJ2cA1trcs/h2Qp5+U0VEpMKlpaVx9OhRAGrUqEGnTp1cjig85c+i5Vu2bBknTpz2XkbCjS8Pvn4CPnsA4/MCcMDW4/qc39L74kn8+pLOeFRGX87PCP/jTGutr/AGf8I0D4gFBpQxzkAgBphXPNHyjzvT37yw0KZBQDvgC+CoMeZSY8yvjDEPGmPCciFNXeIoIiIVrvDsWbdu3YiKCqurUUJKhw4daN68OXv27MHr9TJv3jzGjh1b9oFSNWWfhI9/Bhu/CHSt9bXhnrz/4tEbRnBlzxYuBichpqYxZllJG6y1fco4tqP/cVMp2zfjzLAlAd+c5zj4x8nXz/+4H1gOdC98gDHmR+A6a+3BM5y3StEMmoiIVKicnBzWrl0baOvyxopVfBZt6dKlmkULV8d3w5SxRZKzmXl9mMgzPDtxrJIzCab8m4ZLKw+b31+vAsbJXw/iHpzZt4uA2kA34GucoiEflHHeKkUzaCIiUqHWr19PTk4OAA0bNgxUGpSKk5SURLNmzdi7dy9er5f58+czZswYt8OSYNqzAt69CU7sDXT9y3spr0bfxuTbB9CjZVnvk6UayirHTNm5yr+G1lbAOBGFtl1nrc2vOLXWGHM1zmzccGPMQGvtgvM8f0jQDJqIiFSo4sVBjNG9MBWt+CzakiVLOHnypIsRSVCt/wymXBJIznJtBL/K/RlvxN3B+/cOUXImFSF/Zqu08rt1iu0XzHGO+h+3FkrOALDWZuLMogGklHHuKkMJmoiIVJjia58lJye7HFH10bFjR5o2bQqA1+tlwYKw+GC5erMW5r0A74+H3FMAHLexTMj9FUvqX8YH9w4isVEtl4OUMLXR/5hUyvYO/sfS7i07n3HyjzlGyfITuLBZ4E8JmoiIVJjia59pTa7KU9K9aNnZ2S5GJOclLxdm/BJmPUn+1V/bfU24JudpjjUZxL/vGUgLLUAtFec7/+Nof9n7AGNMbWAwkAksLGOchf79BvuPKzyOB6fQSOHzgbM4tRfoYIyJLmHMbv7H7WWcu8pQgiYiIhVCa5+5r2PHjjRo0ACA7Oxsli9f7nJEck6yjsPb42DZ1EDXYl9Hrs55mgZtuvHuXQOIr1XDvfgk7FlrU3FK4LcFfl5s89NAHPCmtTYjv9MY08kYU2RNFWvtSWCaf//fFRvnfv/4X1trtxY65hDwPs5lkb8tfIAxZhQwBueSyK/O6ZsLQSoSIiIiFUJrn7nP4/EwaNAgZsyYAcDChQtJSUkhIiKijCMlZBzdAe9cDwc3BLo+zhvCY7k/Y2BSc165tQ8x0Xo9pVLcB8wHXjDGjATWA/1x1izbBDxRbP/1/sfiNx4/DlwAPGyM6QksBjoDVwIHOD0BBHjYf64njDHD/Me0Aa4G8oCfWWtLuwSyytEMmoiIVAitfRYakpOTiY2NBeD48eOsW7fO5Yik3HYthddGFknOnsu9lodz7+Wi7q149ba+Ss6k0vhn0foCU3GSpUeAROAFYKC19nA5xzmMs2D1C0B7/zj9gSlAH/95ih9zwL/Pc0Ar4AGcxbM/B4Zaa1VmX0RE5Ey09lnoiIqKIiUlhe+//x6AefPm0a1bN1XTDHVrP4Hpd4M3C4BsG8l/597Fp74hXNOrBX+5rgeREfqcXSqXtXYnMKmc+5b6n4y19gjwoP+rvOc+gjOT9nB5j6mq9JstIiJBp7XPQku/fv2IjHQ+k923b1+gsqaEIGth7j/ggwmB5OyIrcUtOY/zqW8IN6W04q/jkpWciYQx/XaLiEjQFa7eqLXP3BcXF0evXr0C7fnz57sYjZTK53UqNc5+KtCV6mvG1TnPsNR2YuKgtjx7dXc8Hv0+iYQzJWgiIhJUGRkZRWZoevTo4WI0km/AgAGB51u2bGH//v0uRiPFeXJO0vKHh4pUalzo68w1OU+zwzblnuGJPHV5F33YIVINKEETEZGg2rhxI9Y66zS1atWKunXruhyRgHOpaefOnQNtzaKFkGM7aT37Z8TtWxTo+ihvCLflPMZxavHQRUn8amxHJWci1YQSNBERCarCVQILJwTivkGDBgWer1mzhvT0dBejEQD2rIDXRlLjeEHhuudyr+WR3HvJIYr/HtuRBy/qoORMpBpRgiYiIkGTmZnJ1q2B9UWVoIWYVq1a0bp1awB8Ph+LFi0q4wipUBu/hCmXwEnnctNcInko516ez7sWMDx+SSfuu6C9uzGKSKVTgiYiIkGzadMmfD4fAM2aNaN+/fouRyTFFZ5FW7p0KdnZ2awmiDYAACAASURBVC5GU40tfhXeuxlyTwFwglrcmv1rpvuGAvCbSztz17BENyMUEZcoQRMRkaBZv3594HmXLl1cjERKk5SURMOGDQHIzs5m2bJlLkdUzfh88PUT8MWjYJ0PM/Z5mnJV9lMsss6M85OXdeHOoQluRikiLlKCJiIiQZGdnc2WLVsCbV3eGJo8Hg8DBw4MtBcvXhyY9ZQKlnMKPrgNFrwU6NoUmcSlp54i1bYA4HeXd+GOIe3cilBEQoASNBERCYrNmzfj9XoBaNy4MfHx8S5HJKVJTk4mJiYGgGPHjrF582aXI6oGTh6ENy6D9Z8FuhbWGMQVJ3/NYZxKp/cPaMTEwUrORKq7sEzQjDEtjTGTjTF7jDHZxpjtxph/GGPO6mYIY8wQY8yn/uOzjDFpxpgvjDFjKyp2EZGqqvDljZo9C21RUVH07t070F68eLGL0VQDhzbD6xfB7oLLSWfEXs3Nx+8jixoA3D+wEZd31pIUIhKGCZoxJhFYBkwCFgPPAVuBB4EFxpiG5RznXmAOMNL/+BzwAzAc+NIY80TwoxcRqZpyc3PZtGlToK37z0Jf3759A6XbU1NTOXTokMsRhakdC+D1UXB0OwDWeJhc517uPzIOn/9t2NNXdOXyTkrORMQRdgka8DLQGHjAWnuVtfYxa+0InASrI/CHsgYwxkQBfwSygD7W2vHW2l9ba8cDfYFs4AljTI0K+y5ERKqQ1NRUcnNzAWdB5MaNG7sckZSlfv36JCUlBdqaRasAa6fDm1dC5lEAbGQMf6v3JM8cGBrY5cnLujBhUFuXAhSRUBRWCZoxJgEYDWwH/lls81NABjDeGBNXxlANgLrAJmvtxsIbrLXrgU1ADFArCGGLiFR5xRen1qK6VUNKSkrg+cqVK1VyP1ishfkvwgcTIc/5N7VxjXiqwZ95aW/HwG5PXNJZBUFE5DRhlaABI/yPM621RUpSWWtPAPOAWGBAGeMcAA4CScaYDoU3GGOSgA7ASmvt4aBELSJShXm9XjZuLPgsS5c3Vh0JCQmBYi45OTmsWrXK5YjCgC8PvvxvmPmbgq4G7Xm07t94M62gcM6vxnbiZ8NUSl9EThfpdgBBlv+x1KZStm/GmWFLAr4pbRBrrTXG/Bx4C1hmjJkO7AFaAFcDa4EbyxOQMaa0BWZqWmuLvKmpLLrPoHrQ6xz+QuU13rNnT2DmJS4ujvT0dE6cOOFyVOGjol/nNm3aBM4xd+5c6tSpoxnQc2S8WTSb/xtq7/4x0JcRn8yD9lFmb40I9E3o3YARzYp+sBEqv89Ssdx6na21rpxXzk24zaDl32F7vJTt+f31yhrIWvsBzozcMeA24DFgPM5lklNwCo+IiFR7u3btCjxv2bKl3txXMe3atSMy0vm8Nj09nf3797scUdUUkXWUVt/eVyQ5O97qIn4R8SSzdxckZ7f2rM/NyQ3cCFFEqohwm0ErS/67hjI/RjDG3Aq8CnwM/B7YAbQBngRewqnmeH1Z41hr+5QyfoYxJrZjx44lba4Ubp5bKo9e5/Dn5mucl5fHJ598EmgPHjyY1q1buxZPOKvI1zktLS1QJGTPnj0MHz68ws4Vlg6nwtv3wpGCz27twF/wzNFr+Hbz3kDfPcMT+dXYjmf8EEP/Z1cPlf0664OzqiXcZtDyZ8hKq1Vbp9h+JfLfZzYZ51LG8dbaDdbaTGvtBpxZtGXAOGPMBecfsohI1bVjxw4yMzMBqF27Ni1btnQ5IjkX/fr1CzzftGkTR48edTGaKmbXUqeMfiA5M9iL/8LjGdfz0cqC5GzioLZlJmciIhB+CVr+xdxJpWzPL/hR2j1q+UYDUcAPJRQb8QH51y+UODsmIlJdFF6culOnTng84fZnpXpo1KgRCQlOwQprLUuXLnU5oipiwxcw9TI45a8ZFlkTe/2bPL1/CO8u3hnY7aaU1jx1eRclZyJSLuH2l/Q7/+NoY0yR780YUxsYDGQCC8sYJ399s0albM/vzzmXIEVEwoG1tkiCpuqNVVv//v0Dz5cvXx5Y105KseQ1eP8W8DozyMQ0wN72H/68I4mp87cHdrumVwv+cFU3JWciUm5hlaBZa1OBmUBb4OfFNj8NxAFvWmsz8juNMZ2MMZ2K7TvH/3idMaZH4Q3GmJ7AdTj3sX0bvOhFRKqWffv2cfLkSQBiYmJ071kV16FDB+rVc2poZWZmsmbNGpcjClHWwuzfweePQP5FNvXbwh2z+OeWBrzyQ2pg10u7N+Mv1/XA41FyJiLlF1YJmt99OOuYvWCM+cQY80djzLfAQziXNj5RbP/1/q8Aa+1inEqNMcASY8x7xpg/G2PeBxYBNYHnrbVrK/h7EREJWZs3bw48T0xMJCIi4gx7S6jzeDxF7kXLLxoihXhzYPo9MPe5gr7mveGO2UzZGMFfZxbcQXFR5yb848aeREaE41stEalIYfe/hn8WrS8wFegPPAIkAi8AA89icek7gEnAAmCMf5xRwFzgJmvtQ8GNXESkatmyZUvgeYcOHc6wp1QVvXr1CpTc37dvH7t373Y5ohCSlQ7vjIPV7xX0JY2FiTP494Ysnv5sXaB7SPt4Xrq5F1FKzkTkHIRlmX1r7U6c5Ko8+5Z43YF1VvSb6v8SEZFCMjMz2bmzoAhCYmKii9FIsMTGxtKlSxdWr14NwLJly2jRooXLUYWAE/vg7etgX6HLPntPgEv/zudrD/LYR6sD3X3a1Of/butDzSjNKIvIudFHOyIicta2bt2K8zkWNG/enFq1arkckQRLnz4FBYrXrFlDdna2i9GEgIOb4LVRRZOzC5+Ay5/nu81HePC9Ffj8q6t2aVaHyRP7ERsdlp9/i0glUYImIiJnrfD9Z7q8Mby0bt2aRo2cYsW5ubnVu1hI2iKYPBqOpzltEwFXvATD/5sFW49wz1vL8Pqzs8RGcUy7I4W6MVEuBiwi4UAJmoiInBWfz1fk/rP27du7GI0EmzGmyCzasmXLXIzGRRu+gDevgEz/ot1RsXDz+9B7PKt2HuPON5aQ7XWqOLasH8Nbd/anYa0aZxhQRKR8lKCJiMhZ2b9/f5Hy+rpHKfz06NEjUJVz79697Nmzx+WIKtnSKf41zrKcdmw8TJwBHUaxef8JJk5ZTEZOHgCNa9fg7Tv706xujIsBi0g4UYImIiJnpXh5fY9Hf0rCTWxsLF27dg20q80smrXw3bMw45eF1jhrB3fMhBZ92HnkFONfX8zRU84i3vVio3jrzv60aRjnYtAiEm70V1VERM6KyutXD9WuWEieFz57AH74c0Ff815wxyxomMjBE9mMf30R+9KdWbW46AimTkohqUltlwIWkXClBE1ERMpN5fWrj9atWxMfHw9ATk5OeBcLyTnlXNK4/M2CvsSRMGEG1GrE8cxcbpu8mO2HTwEQHeHh1dv60rNVPZcCFpFwpgRNRETKTeX1q49qUyzk1BGnGMimrwr6km9yCoLUqEVmTh53TF3C+r3pAHgMvHhzLwa1j3cpYBEJd0rQRESk3Arff6bqjeEvOTk5vIuFHEuD10fDriUFfUMehqv+FyKiyPH6uPftZSzdcTSw+c/X9mBM16YuBCsi1YUSNBERKRdrre4/q2bCuljI/rVOcnY4/0MHAxf/BS56CozB57M8+sEqvt94MHDIk5d1YVzfVu7EKyLVhhI0EREpl3379qm8fjUUlsVCts+DyRfDib1OOyIarpsM/e8GnA8jnpmxjv+sKpgx/MWI9twxpJ0b0YpINaMETUREyqXw7JnK61cfxYuF/PTTTy5HdJ7WfQrTrobs4047ujbc+hF0uyawy0vfbmHq/O2B9i39W/PwqKRKDlREqiv9dRURkXLR/WfVU/FiIUuXLnUxmvO05HX49wTI888C1moCk76AdsMCu7y9aAd/m7Up0L60ezOeubIbxpjKjlZEqiklaCIiUqbi5fWVoFUvxYuF7Nu3z+WIzpK18N0f4fOHAacKKQ0SnQWom/UI7PbFmr385pOCGcIh7eP5+w3JRHiUnIkAGGNaGmMmG2P2GGOyjTHbjTH/MMbUP8txGviP2+4fZ49/3Jal7L/dGGNL+api/yGVLdLtAEREJPQVLq/frFkzldevZmJjY+ncuXPg8sYVK1Zw8cUXuxxVOfny4ItHYenkgr7mveCWDyGuoFT+vC2H+OV7K/H/mNOjZV1eGd+HGpERlRywSGgyxiQC84HGwKfABiAFeBAYa4wZbK09XI5xGvrHSQK+Bd4DOgGTgEuNMQOttVtLOPQ48I8S+k+ew7cT0pSgiYhImVS9UXr16hVI0FavXs2oUaOIjAzxtxG5WfDxz2D9fwr6EkfA9dOgRsGHDGt2HeeuN5eSk+cDIKFRHFMm9qNWjRD//kQq18s4ydkD1toX8zuNMX8HHgL+ANxTjnGexUnOnrPWPlxonAeA5/3nGVvCccestb875+irEF3iKCIiZ1S8vL4ub6ye2rVrR926dQHnktdNmzaVcYTLstLh7euKJmfdroOb3i+SnG07lMHEKYvJyMkDoGmdmky7oz8Na9Wo7IhFQpYxJgEYDWwH/lls81NABjDeGBNXxjhxwHj//k8V2/ySf/wx/vNVW0rQRETkjA4cOMCJEycAqFmzJi1blniLgIQ5j8dDcnJyoL1ixQoXoynDif0w9RLYPqegr/+9cM2rEBkd6DpwIovbJi/icEYOAHVjoph2Rwot6sVUdsQioW6E/3GmtdZXeIO19gQwD4gFBpQxzkAgBpjnP67wOD5gpr95YQnH1jDG3GqMedwY86Ax5kJjTFheg6y5exEROaPt27cHnrdr107l9auxnj178uOPPwLOZa/p6enUqVPH5aiKObLNKaN/dFtB38inYMhDUKgS44msXCZOXsLOI5kA1IzyMHliXzo0qV3ZEYtUlprGmBJXm7fW9impv5CO/sfSps4348ywJQHfnOc4+McprikwrVjfNmPMJGvtD2c4Z5Wjv7IiInJG27YVvNFt104L9VZnDRo0oG3btoBz6evq1avdDai4fWtg8piC5Mx44IoXYejDRZKzbG8ed09bxrq96QBEeAwv3dSbPm0auBG1SFVQ1/94vJTt+f31KmicKcBInCQtDugO/AtoC3xpjEkmjGgGTURESuXz+YrMoOW/OZfqq1evXoGfiRUrVjB48ODQWCNsx3x458aCBagjasC4KdDp0iK7+XyWh/+9ivmpBcXm/nh1dy7q0qQyoxVxQ1Y5ZsrOVf5/ArYixrHWPl1sv5+Ae4wxJ4FHgN8BV5/nuUOGZtBERKRU+/fvJysrC4C4uDgaNWrkckTits6dOxMd7dzHdfjw4SLr47lmwxfOZY35yVmNOjB++mnJmbWWZ2as4/PVewN9/zWmI9f3a1WZ0YpURfkzW3VL2V6n2H4VPU6+V/yPw864VxWjBE1EREpV+PLGtm3bhsZMibgqOjqabt26BdquFwtZ8Ta8fyt4nQ8SiGsMk76AtoNP2/V/f0hl6vztgfaEgW2474LESgpUpErb6H8s6d4wgPz1V8oq7xqscfId8D+esXpkVaMETURESlW8QIgIOJc55lu7di05OTnuBDLvBfj0PrBOiXzqt4U7voam3U/b9cNlu/jLVxsD7Ut7NOO3l3fVhw4i5fOd/3G0MaZI/mCMqQ0MBjKBhWWMs9C/32D/cYXH8eAUGil8vrIM9D+WtLB1laUETURESpSXl8eOHTsCbd1/JvlatmxJfHw8ADk5Oaxbt65yA7AWZv0WZj1Z0NekO9w+ExqcvnzS9xsP8NhHBQVNBiY05O/XJxPhUXImUh7W2lScEvhtgZ8X2/w0zgzWm9bajPxOY0wnY0ynYuOcxKnEGIdz31hh9/vH/9paG0i4jDFdjTGnVfAxxrTBWTsN4K2z/qZCmIqEiIhIifbt20d2djYAtWvXpmHDhi5HJKHCGEOvXr2YNWsW4Fzm2LNnz8o5uS8PZvwSlr9Z0Nd6ENz0LsScXkBu9a5j3Pf2crw+p+ZAp6a1+ddtfagRGZbLJ4lUpPuA+cALxpiRwHqgP86aZZuAJ4rtv97/WPyTkMeBC4CHjTE9gcVAZ+BKnEsWiyeA44DHjDHfAduAE0AicClQE/gC+Ot5fm8hRTNoIiJSIt1/JmfSo0ePwM/Ejh07OHz4cBlHBEFuFnwwoWhylnQxjP+4xORsx+EMbp+6hFM5ziWQLerF8MbtKdSpGVXxsYqEGf8sWl9gKk5i9ghOovQCMNBaW67/BPz7DfQf194/Tn+cUvp9/Ocp7DtgOtAOuBl4GBgOzAUmAJdZa126zrpiaAZNRERKpPvP5Exq165Nhw4d2LTJuZd/5cqVjBw5suJOmH0C3rsZtv1Y0Jd8E1zxEkSc/nbm0Mlsbpu8mEMnnfdtdWOieOP2fjSpU7PiYhQJc9bancCkcu5b6qd61tojwIP+r7LG+QEIq4Woy6IZNBEROY3uP5PyKFwsZOXKlfh8voo5UcZheOPyosnZgPvgypdLTM4ysr3cPnUJOw6fAqBGpIfJE/vSvnHt0/YVEQk1StBEROQ0e/bsITc3F4C6detSv359lyOSUJSUlERsbCwAJ06cKHJZbNAc3wVTxsKeQuX8RzwJY54Fz+lvY3LzfPz8neWs3uUso+Qx8OJNvejT5rQaAyIiIUkJmoiInKbwG+127drp/jMpUUREBD169Ai0V61aFdwTHNoCk8fCofwlkQxc9hwMexRK+Jm01vLE9DV8v/FgoO/3V3VjdNemwY1LRKQCKUETEZHTFL7/TJc3ypkkJycHnq9fvz5Q+fO87V0Fk8fA8Z1O2xMF102GvreXesg/Zm/m30t3Bdq/GNGeW/q3CU48IiKVRAmaiIgU4fV6SUtLC7RVIETOpGnTpjRu3BiA3Nxc1q9fX8YR5bBjPky9DE4dctpRsXDze9DtmlIPeW9xGs9/sznQvrZ3Sx4elXT+sYiIVDIlaCIiUsSuXbvwer0A1K9fn7p167ockYQyY0yRWbTzvsxx00yYdjVkpzvtmnVh/CfQ/qJSD/luwwGe+OSnQHtoh3j+dG13XZorIlWSEjQRESlC5fXlbHXvXpAMbdu2jWPHjp3bQGs+hPduAm+W045rDBO/gNb9Sz0kfyHqPP9C1F2b1+F/b+1DVITe4ohI1aT/vUREpIjiC1SLlKVOnTokJCQE2mvWrDn7QZa8Dh/dCT5n9pZ6reH2r6Bpt1IPSTt8itunLiEzt2Ah6ikT+1GrhpZ5FZGqSwmaiIgE5ObmsmtXQZEFzaBJeRW/zNFaW/6D5z4Hnz8M+I9p1Alu/xoaJpZ6yJGMHCZMKb4QdQqNtRC1iFRxStBERCRg586d5OU5sxENGzakdm0t7Cvl06lTJ6KjowE4dOgQe/bsKfsga2H275yvfM17w6QvoU7zUg/Lys3jzjeWsO1QBgDRkR5en9CX9o1rncd3ICISGpSgiYhIgO4/k3MVHR1Nly5dAu2VK1ee+QCfz5k1m/tcQV/boTDhPxBb+qLSeT7LL99byfI05z43Y+D5G3rSt60WohaR8KAETUREAoovUC1yNgpf5vjTTz8FqoGeJi8Xpt8FSycX9CVdDLd8CDVKn7W11vL7Gev4au2+QN+Tl3bh4u7Nzjt2EZFQoQRNREQAyMnJYffu3YG2CoTI2WrTpk1gWYbMzEw2b958+k65WfD+eFjzQUFf9+vhhmkQdeb7x16fu42p87cH2ncMacftQ/RBgoiEFyVoIiICOPef+Xw+ABo3bkxcXJzLEUlV4/F46NGjR6B92ppo2Sfg7etg05cFfX3vgKv/BRFRZxz789V7+Z/PCxbBvrhbU564pHNQ4hYRCSVBrUNrjGkBDPN/dQXigUb+zQf9X2uBOcCP1trdJY0jIiKVLy0tLfC8devWLkYiVVlycjJz5swBYNOmTZw6dYrY2Fg4dQTeHge7lxbsPORhGPlb50ayM1iy/QgP/bvgnrY+berz3A098Xi0ELWIhJ/zTtCMMXHAjcCdQErhTcV2bQh0AoYAd/uPXQy8Brxnrc0431hEROTc7dy5M/BcCZqcq/j4eFq0aMHu3bvx+Xz89NNPpHRuA9OuhgNrC3a86Hcw5KEyx0s9eJI731hKjteZ3U2Ij+O12/pSMyqiYr4BERGXnXOCZoypA/wK+AUQR0FC5gXWAFuBo8ARf38DoD6QAHT3n7s/TlL3nDHmReDP1tr0c41JRETOjc/nK7L+WatWrVyMRqq65OTkwP2Mq5YvIWXhPXAktWCHS/4KKT8rc5yDJ7KZOGUxxzNzAYivFc3USSnUj4uukLhFRELBOSVoxpiHgV/jJF0G2Ay8C3wNLLfWZpdxfA2gFzAauBlIAh4D7jLGPGutfe5Mx4uISHAdOHCAnBxnwd/atWtTr149lyOSqqxbt2589dVX+Hw+du87yCGOEA9gIuCqlyH5xjLHOJXj5c43lrDzSCYAMVERvD6hH60bxlZs8CIiLjvXIiF/BeoCbwB9rbUdrbW/s9YuKCs5A7DWZltrF1prn7HWdgL6+Meq6x9bREQqUeH7z1q1aoUp454gkTOJjY0lqXXTQHs1nSAiGq5/o1zJWZ7P8sC7K1m16zgAHgMv3tSL5Fb64EBEwt+5JmivAknW2tuttcvPNwhr7Qpr7e04M2mvnu94IiJydgrff6bLG+W87VpGj91vBZpr6Iy98V3ofHmZh1preeaztcxevz/Q97srunJRlyYVEqqISKg5pwTNWnu3tXZ7kGPBWrvdWntPsMcVEZEzU4ImQbN9Hrx5BR1yf6IGWQAcpS67anYs1+Gvz93GGwt2BNp3D0vgtoFtKyJSEZGQpHXQRESqufT0dI4dOwZAZGQkzZo1czkiqbK2zIa3roWck0SRR5eIgktnV69eXebhxdc6u7RHM341tlOFhCoiEqpcT9CMMbXcjkFEpDorPHvWokULIiJUvlzOwfrP4J0bwesU9aBWE3pcdndg808//UReXl6phy/bUXSts35t6/O3ccla60xEqp2gJWjGmHf9pffP5pjBwKpgxSAiImdPlzfKeVv1Pvx7AviccvjUbQWTvqRN8lDq1HHeGmRmZrJly5YSD992KKPoWmeN4nhVa52JSDUVzBm0G4DVxpjhZe1ojIkwxvwP8D3QNogxiIjIWVKCJudl6RSYfjdY/+xYg0SY9CU0TMTj8dC9e/fArmvWrDnt8MMnnbXOjp5ykruGcdFMnZhCvVitdSYi1VMwE7QMoDXwjTHmz8aYqJJ2MsYkAQtx1lGLAJYFMQYRETkLOTk57N27N9BWgiZnZcHLMOOXgHXajbs4yVm9gp+jwgnahg0byM4uWI0nKzePn725lB2HTwFQM8rD6xO11pmIVG/BTNB6Aov8Yz4KLDLGdC68gzHmXmA50Bvnf/NngUFBjEFERM7Cnj178Pmcy8ri4+OJjdUbYymnH/8ffP3rgnaznjDxc6hdtBx+06ZNady4MQBer5f1650iID6f5aH3V7I8zSlQYww8f2MvemqtMxGp5oKWoFlrU4HBwNNAHk7CttQYc78xpokxZgbwEhAL7ACGW2t/Y631BisGERE5O7q8Uc6atfDNM/Dt/xT0tRoAE/4DsQ1KPKRHjx6B5/mXOf7pqw18+dO+QP+Tl3ZhTNempx0rIlLdBLWKo7XWZ619GhgKpAIxwPM4CdnFgAGmAcnW2nnBPLeIiJy9wgla69atXYxEqgRr4evHYc7fCvraDYPxH0PNuqUeVvgyx61btzLl+3X8349bA30TB7Xl9iHtKiRkEZGqpkLK7FtrF+HMph30d+Xf6fuEtXaCtfZERZxXRETKz+fzaQZNys/ngxkPwcKXC/o6jIab/w3RcWc8tG7durRp0wYAay0fzl4Q2Da6SxOevKxLhYQsIlIVVUiCZozpC/wIxOPMmuF/fNwYc1dFnFNERM7O4cOHycx01qyKiYmhYcOGLkckISvPC5/eB8umFPR1vgJueBuiYso1ROHLHNt5DgOQ3LIuz9/YiwitdSYiEhDUBM04HgfmAUlADk7BkOE4lznGAf9rjPnUGNMomOcWEZGzU3z2zBi9SZYS5OXCx3fCqncL+rpfD9dNgcjyl8Kv16Idef7PbOM9p0iqa3ltQj9iorXWmYhIYcFcqLo18APweyAK+AlIsdb+3Vo7B+gBvIUzk3YZsMYYc0mwzi8iImcnLS0t8Fz3n0mJvNnOAtRrpxf09b4Nrn4FIiLLPczxzFzufXcNO/MKKjTe1S2SRrVrBDNaEZGwEMwZtNU4952BUxikn7U2sCKltfaEtfY2nAWtjwGNgc+MMS+fNpKIiFQ43X8mZ5SbCe/dDBs/L+hLuQsuex485Z/1yvH6uPetZWzaf5KteQVVHnelbsBaG8yIRUTCQjATtDrAPmCstfYha212STtZaz8AugPf4sym3R3EGEREpBwyMjI4fNi5D8jj8dC8eXOXI5KQkpMB71wPW2YX9A16AC7+C3jK/9bBWsvj09cwP9X5Wdvtq0dElHNZ5LFjx4p8SCAiIo5gJmjTge7W2lll7Wit3WOtvQjn/rScIMYgIiLlsGvXrsDz5s2bExUV5WI0ElKy0uGta2HbjwV9w38Fo55xVpM+Cy9+u4UPlxX8rP1yVCeSu3cLtPPXRBMRkQLBXKj6WmvtkbM85u9Av2DFkM8Y09IYM9kYs8cYk22M2W6M+Ycxpv45jNXdGPOmMWanf6wDxpgfjDG3BTtuEZHKUvj+M13eKAGZR2HaVZBWUAafkb+FCx8/6+Rs+opd/H3WpkB7XJ+W3D+ifZE10dauXUteXt55hy0iEk4qpMz+2bDW/hTM8YwxicAyYBKwGHgO2Ao8CCwwxpS7jrQxZiKwArgKmAP8DfgQ59JMFTgRkSpL95/JaU4dgTeugN3LCvrG/BGGPnLWQy1IPcx/f7g60B7SPp5nr+mOMYY2bdpQu3Zt55SnTrFt27bzDl1EJJy4nqBVrfN1hgAAIABJREFUgJdxCpA8YK29ylr7mLV2BE6i1hH4Q3kGMcYMAF7DqUaZZK292dr/z959h8dVXI0f/x51Wc2WbblX3Hs3htATBwgtdAzGhRogECDvL0DeEEgj5A0lQCBUVzAtlASHGggBdxv33qvkbkuyunR+f9yr3bVstd0r7Uo6n+fZZ3dumRkho92zM3NGH1LVO1T1TGB8HfXfGGPqVElJCXv27PGVLUAz5O6HqRdBlj+o4kdPwJg7al3Vpn053DZjMcWlTgKQXm2Sef6GYcRGOx85oqKiGDDApjka0xB5NUtNRNLd+7a59exx6+1Yw/vHi4i6j5uD+2kiV1ABmojcLSKe58YVkQQRuSeE+7sDY4FtwF8rnP41cAwYLyJJNajuT0A0cIOqZlU8qarFwfbTGGPCKTMzk5KSEgBatGjhG80wTVROFkz9Eexb7R4QuOQ5GFn7zzz7cwqZOGUR2QXOv6/WKfFMmTSK1ITj1zgGTnNcu3YtxcX2lmpMpPNqlpp73Tz3vs1uPQvdepe4n+erur8T8CyQG9xPEvmCHUF7GtgiIveKSMjv7CKSJiL3A1uBJ0Oo6lz3+TNVLQs8oao5OBtoNwNOraY/HYEzgMXAahE5R0R+LiL3i8h5ItIYRx6NMU1EYIIQGz1r4rL3OMHZgfVOWaLgxy/CsNpPEskvKuXmaYvYdTgfgGZx0UyZOJIOzRNPuLZdu3a0bOl8lisqKmLDhg0nXGOMiTiezFID/gD0Ap5S1fPcei7DCdgy3HZOSkQEmAIcBP4W/I8S2Wq+y+TxpuJM8fsz8HsRmQ3MwgmMahTNikgazmjXdcAFQBxQhvMfPVi93efK/tJvdNvsBfy7inrKE5dsxNkO4OwK51eKyOWquqm6DonIkkpOJagq69evr64Kzx04cKDe2zT1z37PjV+wv+N169b5XsfGxobl75Cpubr6fznmWCadvryDuNzdAKhEkznmN+QkDIFa/psoLVN+/1UWy3cdAyBK4BdnZhCbm8X69SdMQgGcIK18q4d58+YRExPsR5LGwf5mNw3h+j2HuudgDWap3YozS+1+VT1WRT1JODHEMfe+QM8B9wI/FJHuqrrlJFXcjTMgczb+gZlGJ6i/hqo6WUSeAP4I/Ai4ArgcUBHZCCzCGfI87D4A0oEWwCk4AVAP93h5Wqh/Ag+o6tpg+uRKc5+PVnK+/HjzaurJcJ+vBg7g/Gz/Blrj/GMaD8wWkYGqatsEGGMalPIPxQDp6elVXGkaq9jc3XT68g5ij2UCoFEx7Dnt9+R2Oieo+l5ZfIA5O/yfyX4yuhWndqp6NUGXLl1YtcrJE7Znzx6KioqIi4sLqn1jTJ2rcpaaiMzBCeBOpepBkDFAoltPToV6ykTkM5xg7xycWMJHRPrixB5/UdX/iogFaBWp6mrgYhEZgPMfchxOENYbZ4SqKuVB2SFgJvCyW19dK2+3uq8RogOeb1bVj9xytohMAPoCI3AC01lVVaSqw0/aEZFjItKsd+/eJztdL8LZtqk/9ntu/GrzO87Pzyc315noEBUVxahRo2wPtAbCs/+XD26G2XeBG5wRHYdcPYMOvc8Pqrppc7fx3mr/96I3f68b/3NRvxrd+91335GZmUlZWRnFxcXHrU1rquxvdtNQ379nZ2YgCZXN7Krs82oAr2ap1aQeqBBLiEgMMAPYATxUTV8bvJDXUqnqKlW9G+iAk3r+MZy1XuUjZ4I/MDrsnnvMvbaDqv7Mw+Cs/B0irZLzqRWuq0x53wuBfwWeUGeM+EO3OKq2HTTGmHAKzN7Ypk0bC86amgMbnTVn2c60RmIS4LpZEGRw9vmavTz6T/9b+Pn92/LQhX1rfH9gQFY+mmaMiUhezVILtp6HgaHARFXNr6aNBs+zCd+qWgh84j4AcJNplGd0OVhxSLQOlE+ar2wEr6f7XN1q5PJ6cirpc3kAd+LKZ2OMiWC7d+/2ve7QoUMYe2Lq3f71MO1iyN3rlGMSYdyb0P3soKpbuesod89aSpk7J2Vwp+Y8dc0QoqJqvqF1//79+eyzzwDYunUrOTk5llXUmLpTUIORsmDVdJZaresRkVE4o2ZPqOq8EOtvEOo0G6GqlqnqfvdR18EZwFfu89iKmRbdbJOnA/nA/GrqWYGz9qyViLQ5yfnyDVy2Bd9VY4ypf4EBWvv27cPYE1Ov9q5xRs7Kg7PYZnD9O0EHZ7sO5zF52iLyi0sB6JSeyKsTRpAYF13NncdLS0uja9eugJPEYPXq+ljtYIwJglez1GpVT8DUxg3Ar6rvZuPQqNLFq+pm4DOgK3BnhdOPAknA9MDsMiLSR0T6VKinBHjRLf4pMNgTkYHARKAEeNfjH8EYY+pU4BRHG0FrIrJWwrSL4Nh+pxyXDDf8HbqdEVR1R/OLmTx1EftzCgFITYhhysRRtEoObnvUwGmOtmm1MRHL61lqNa0n2b22L1AQsDm14s8C+bJ77Olq2m4w6iSnrYhE4yQMEeCoO/2xvtwBzAWeEZHzgLXAaJxsMBuAX1a4vjxrZMU5GX8AzgNuBAaKyH9wsjheASQA99ckzb4xxkSK7OxscnKcpFmxsbG0atUqzD0ydS5zOUy/FPLdmflxKU5w1nl0UNUVlZTxk5lL2LDXSTQTGy28dOMIemQkB93Fvn37Mnv2bMrKyti9ezeHDh2y7KLGRJ7jZqkFzoyr5Sy1+e51p4tISmAmR3dAZGyF9gqBVyupaxjOurRvcQK/RjP90ZMRNBGJEpFrRORNEdkJFAFZQCaQJyLb3XNX1vUmz+4o2gicvdpGA/fjpPZ/Bhijqgcrv/u4evJwArRHcTa3vhO4BCf4u1BVQ9lQ2xhj6l3g6Fm7du2Ijq7ddDTTwOxZCtMu8Qdn8Wlw4wdBB2eqykPvr2TuZv/b6P9dOZhTu7es4q7qNWvWjB49evjKNopmTOTxcJZaLs6UxSTgkQr13OXW/2n5Hmiqmq+qN5/sAfzDvW+ae+wtD37UiBDyCJqI/AB4GehUfugkl3UCOgJXAVtE5FZV/ariRSKSVNXmdjWlqjuBSTW8ttLVzG6Q9ggn/gMyxpgGxxKENCG7l8CMH0OBu9wjIQ3GfwAdhgVd5XNfbuLdJbt85ft+0IvLhnrz72jgwIFs2ODMaFq5ciVnnnlmeVpwY0zk8GqW2kM4G03fJyJDgIU4UxgvBfZxYgDY5IQ0miUi/wN8jBOAlafT34GTyfFN4C339faA86cAn4vI7RXqygC+DqU/xhhjKhc4gmYJQhqxXYthemBw1hxu/EdIwdn7S3fxxOf+pSVXDu/IT8/tUcUdtdO7d2/flg8HDhwgKyvLs7qNMd7wcJbaQZwNq58Berj1jAamAMPddpq0oEfQRGQ88LhbzAWeAF5zR69Odn1HnFGtnwMpwHMisk1VPxGR7jjDpt2C7Y8xxpjKqaqNoDUFOxfBzMuhMNspJ7ZwgrN2g4Kucv6Wg/y/d1f4yqf3aMkffjzQ0xGuuLg4+vTp45veuHLlStq1a+dZ/cYYb3g4S+0QcI/7CLYvj9BIZ7kFNYImIs2B8jVYq4B+qvpoZcEZgKruUtXfAv2AlW7bfxOR03GGS7vjZEY0xhjjsUOHDlFQUABAYmIiLVq0CHOPjOd2LHCmNfqCs3SY8M+QgrNN+3K4dfpiikudLYl6tUnm+euHExfj/XLywGyOq1evpqysPnbnMcaYyBPsX9iJOBtQHwS+r6q7qr7cT1V3Az9w7+2EM60xAygALg+yP8YYY6pQcXqjre9pZHbMd0bOityEaM1awcSPoO3Aqu+rwv6cQiZOWUR2gfPdaeuUeF6bOJK0xFgvenyC7t27k5iYCMDRo0fZtavGHy2MMaZRCTZAuwhnh+8/q+q+2t7s3vMEzpq0KCAbOF9VZwfZH2OMMVWwDaobse3zYMblUOSkvieptROctekfdJX5RaXcPH0xuw7nA5AYG81rE0bSsUUzL3p8UjExMfTt29dXtmyOxpimKtgArbf7HEpA9ZH7rMA5qvrfEOoyxhhTBdugupHaPhdmXgHFbgLkpAyY8BFk9K36viqUlik/e2spy3ceASBK4LlxQxnYMc2LHlcpcJrjmjVrKC0trfM2jTEm0gQboLV2n3dXeVXVyj8tqKouDaEeY4wxVSgtLSUzM9NXtgCtkdg2B2ZeeXxwNvEjyOhT9X3V+MO/1vLp6r2+8qOX9Oe8vm1CqrOmunTpQnKys+n1sWPH2Lp1a720a4wxkSTYAK181+9Qvk5LdZ+PhFCHMcaYahw4cIDi4mIAUlJSSElJCXOPTMi2zYHXr6oQnM2G1r2rvq8aU+ds5dVv/UHRLWd0Y/yYriHVWRtRUVEMGDDAV161alW9tW2MMZEi2ACtfOTs1BDaHu0+2ypgY4ypQ5Zev5HZ9i28HjByltzGDc56hVTtZ6uzePSjNb7y+f3b8uAFwU+VDFZggLZ27VrflwvGGNNUBBugfYGT4OOnwdwsTvqwe3DWn30RZB+MMcbUgG1Q3Yhs+9YdOctzysltnDVnIQZny3ce4e43l6JONn2Gdm7O09cOISqq/rN9dujQwbcNRGFhIZs2bar3PhhjTDgFG6DNxAmuThWR/wvi/j/ijL4pMCPIPhhjjKkBG0FrJE4Iztp6MnK281AeN01bREGxs+9Y5/RmvHLjCBJio0PtcVBE5LhRNMvmaIxpaoIK0FR1GU5gJcB9IvKBiHSt7j4R6SIi7wE/xw3OVHV5MH0wxhhTveLiYvbu9Sd8sBG0hilx33cnCc4+glY9Q6r3aF4xE6cs5EBuEQDNm8UyddJIWibHh9rlkARmc9ywYQOFhYVh7I0xxtSvmBDu/QlOuv3RwMXARSLyNc7G02txkn8o0ALoA5zlPqJwArv5wB0htG+MMaYae/fupazMGRlJT0/3bQRsGo7EfUvp+PW9UOLsSeZVcFZYUsqtMxazeb+zli0uJoqXbxxB99bJoXY5ZBkZGWRkZLBv3z5KSkpYt24dgwcPDne3jDGNhIh8hxOnnKaqhe6xzgCquiOcfYMQAjRVzReRHwIvAtfgBF1nu4/KlE9mfxO4XVXzg23fGGNM9Wx6YwO3fS4dv/4ZUb7grI0nwZmq8ot3V7Bg6yHfsSeuGszIrukh1eulAQMG8OWXXwJONkcL0IwxHhqCE6AFzuXeBpSJSKqq5oWlV65g16ABoKrZqnodcAHwKVCGE4Sd7FHmXnO+qo5T1exQ2jbGGFM9SxDSgG2fBzOvPD44mxB6cAbwxGcb+GCZ/9/GL87vw8WDI+vfR+A6tM2bN5OXF9bPS8aYxqXMfa44WFX/mZFOIpQpjj6q+inwqYgk4yT/6IYztVGAQ8BWYL6q5nrRnjHGmJqxEbQGasf841LplySkE+NBtkaANxfu4Lmv/JkRx43uzO1ndQ+5Xq+lp6fToUMHdu/eTVlZGWvWrGHEiBHh7pYxpnE4BLQEegDfhbkvJ/AkQCvnBmCWNt8YYyJAYWEhBw4cAJzMeG3btg1zj0yN7FwIM6+AIuc7zZKEdHae+wLdPAjO/rN+H7/8wL/58zm9W/ObS/rj7H4TeQYOHOj7kmHVqlUWoBljvLIEGAtMFZGXgaMB564XkVplJlLV6V52ztMAzRhjTOQInN6YkZFBXFxcGHtjamTXYphxuS84I6k1O896lqK0biFXvXrPUe58/TtKy5zNzgZ0SOW5ccOIiQ5ptUOd6t+/P59++imqyrZt28jOziY1NTXc3TLGNHx/AX4I9AeeDjguwN9qWZcCngZokftX2RhjTEhsemMDs/s7NzjLccrNWsGEf1KUFvr0w91H8pk0ZRHHikoB6NA8kdcmjCQpPrK/p01JSaFr166+8urVq8PXGWNMo6GqnwCXAwuBfJzATN3TleXTqOzheTxlAZoxxjRSmZmZvteWICTC7VkGMy6DQneWTbOWMOEfkNE35KqzC4qZPGUR+3KcGTspCTFMmTSSjNSEkOuuD7ZptTGmLqjqB6o6RlWTVbV8GzAFklU1qjYPr/tmAZoxxjRSWVlZvte2/iyCZS6H6ZdCgRucJbaAGz+ENv1DrrqopIyfzFzC+r3OqFxstPDi+OH0apMSct31pW/fvkRFOR9X9uzZw6FDh6q5wxhjGjYL0IwxphEqLCzk4MGDgJMgpE2bNmHukTmprJVucHbEKSc0hxv/AW0Hhly1qvLAeyuYs+mg79ifrhzEaae0Crnu+tSsWTN69OjhK69ataqKq40xpnoi8qSIPCEigfO8z3EfYd+n2QI0Y4xphPbu3et73apVK2JjY8PYG3NSe9c4wVn+YaeckOaMnLUb5En1T36+gfe+869DvP8Hvfjx0I6e1F3fbJqjMcZjP3MfgdmzpgJTgPhwdCiQBWjGGNMI2fTGCLd/PUy/BPLc0a34NBj/AbQf4kn1by7cwbNf+vc6u3ZkJ+46t0cVd0S23r17ExPjfNG9f//+476AMMaYIAQmBCnXBehKBMRHYe+AMcYY7wUGaO3atQtjT8wJDmyEaRfDsf1OOS4Fxr8HHYZ5Uv1XFfY6O6tXa3572YCI3eusJuLj4+ndu7evbNMcjTEhcvcyISK/wbQAzRhjGiEbQYtQBzc7wVmuOwIUlww3/B06erMB86rdx+911r99Kn+9fhixEbzXWU0FTnNctWoVqlrF1cYYU6W17vPvRWSAiHQOONdJRDrX5uF15yJ7AxRjjDG1VlpaetwUMAvQIsThbTDtEshxtz+IbQbXvwOdR3tS/c5DeUyauoi8gL3OpkwcSXKE73VWUz179iQ+Pp7CwkIOHz7M7t276dixYa6pM8aE3QxgFHCV+ygnwJpa1qV4HFM1/K/UjDHGHOfAgQOUljof0lNTU2nWrFmYe2Q4sgOmXgzZu5xyTCKMewu6nOZJ9Ufzipk0dRH73b3OUhNimNqA9jqriZiYGPr29e8LZ9McjTEheB74C1CCf8PpcrXdqNrz+eNBRXsi8rDXHamMqv6mvtoyxpjGwNafRZiju51pjUd3OOXoeLhuFnQ705PqC4pLuWXGYjbtc5ZUxEVH8dKNI+jZgPY6q6kBAwawbNkywAnQxo4d69sjzRhjakqdOdL3isivgD5AEvAVzmjYjwhzqv1gh+MewZ/9pK6U7+ZtAZoxxtRCZmam77VNbwyznCwnODu8zSlHx8G1b8Ap53hSfVmZcv87y1m41b958/9dNYhTu7f0pP5I061bN5o1a0ZeXh65ubls376dbt26hbtbxpgGSlVzgcVAYCKl/6pqXtg6RfAB2nTqPkAzxhgTBEsQEiFy9ztrzg5tdspRMXD1dOj5fc+aeOzjtcxe4Q/IH7ygD5cO6eBZ/ZEmOjqa/v37s2jRIsAZRbMAzRjjkd/gxDdF4e5IUAGaqk70uB/GGGM8oKo2xTES5B1yNqE+sN4pSzRcOQV6X+BZE699u5WXv9nqK08Y04Vbz+zuWf2RasCAAb4Abc2aNVxwwQW+PdKMMSZYqvpIuPtQziZuG2NMI3L06FEKCgoASEhIIC0tLcw9aoLyj8CMy2DfaqcsUXD5S9DvEs+a+HhlJr+d7U809sP+bXj44v4Neq+zmurUqROpqakA5Ofns2XLljD3yBhjvGVfORljTCNScf1ZU/jAHlEKsmHm5ZC53D0gcNkLMPBKz5pYvO0Q97y1jPJtwIZ1bs5frh1KdFTT+F1HRUUxYMAA5s6dCzjTHHv16hXmXhljGhIRubH8tapOr3istsrr8IoFaMYY04jY9MYwKsyFN66G3Uv8xy55BgZf61kTm/blcvP0xRSVlAHQvVUSr0wYSUJstGdtNASBAdq6desoKioiLi4uzL0yxjQgU3HWmylObo3AY7UVWIcnbIqjMcY0IpYgJEyK82HWtbBjnv/YhX+GYUF/IXuCfdkFTJyykCN5xQC0So5j6qRRpCc1vcCkXbt2tGzpZKosKipi48aNYe6RMaYBEk6MhYLZA83zeMoCNGOMaUQsxX4YlBTCWzfAtm/8x374GIy6xbMmjhWVMXHKInYddrbmaRYXzWsTR9K5ZdPchFxEGDBggK+8cuXKMPbGGNPQqGpU+eNkx2r78Lp/wW5UXV8rclVVT6mntowxpkHLy8sjOzsbcNKRt2rVKsw9agJKi+GdSbDpC/+x834NY+7wrIniUuW3X2WyJtMJzqKjhL9eP4xBHZt71kZDNGDAAL7++msANm7cSEFBAQkJCWHulTHGhC7YNWhdvexEFWyvNWOMqaHA6Y1t2rQhOrpprUuqd2Wl8N6tsH62/9hZv4Az7vOuiTLlyW/3snRPvu/YY5cP5JzeGZ610VC1bt2atm3bkpWVRWlpKWvXrmXo0KHh7pYxxoQs2ADtHE97YYwxJmS2/qwelZXBh3fC6vf8x067G85+0NNm/vTper7ckusr3/+DXlw9opOnbTRkAwcO9P27X7VqlQVoxpgaEZHOXtanqju8rC/Yjaq/9rITxhhjQmfrz+qJKsy+D5bP8h8bdRv84Dfg4bYGU+ds5W9fb/aVx43uzF3n9vCs/sagf//+fP755wBs2bKF3NxckpOTw9wrYxovEekI/AY4H2gJZAIfAI+q6uFa1JMOPAxcBrQDDgKfAA+r6q6TXP84MALoBbQC8oHtbtvPqerBWv4oW2t5fVUUjzPjW5IQY4xpJCzFfj1QhU8ehCVT/MeGTYALHvc0OPt4ZSaPfuTfiPrUTkn85pKmsRF1bTRv3pzOnZ0vwlWV1atXh7lHxjReInIKsASYBCwEngK2APcA80SkZQ3raQnMc+/b7Naz0K13iYh0P8lt9wJJwOfAX4DXgRLgEWCFiNR2akEw2RqrenjK9kEzxphGoLi4mAMHDvjKGRm2RqlOfPlbWPCCvzzoWrjoaU+DswVbDh63EXXf1vE8eHYbYqLtO9WTGThwIDt2OLOLVq1axejRo8PcI2MareeBDOBuVX22/KCIPIkTQP0euL0G9fwBZyTsKVX1LdoVkbtxgq/ncUboAqWqakHFikTk98BDwINAbbIzVbZcKx14AiffxkLgfWAdkAskA31wRv1G44zC3Q/UeOSwpuyvvTHGNAJ79+5F3U/0LVu2JD4+Psw9aoT++2f45gl/ud+lcOlfIcq7t9J1WdknbET96PfbkxBjb9eV6devn29kcefOnRw+7PlnJWOaPHdUayywDfhrhdO/Bo4B40UkqZp6koDx7vW/rnD6Obf+H1YcRTtZcOZ6233uWfVPcDxV/briA1gM/BZnyuUNqnqqqj6uqh+q6r/d58dVdQxwA9DBvX5xbdquCfuLb4wxjYAlCKlj8553Rs/K9fwhXP4KRHs3EWX3kXwmvraInIISAFqnxDNt8ijSEiwbZ1WSkpI45RT/jjyrVq0KY2+MabTOdZ8/U9WywBOqmgPMAZoBp1ZTzxggEZjj3hdYTxnwmVusaULCi93nFTW8vir/A/QFfqeqb1R1oXv+d0B/4BcetH0cC9CMMaYRsPVndWjxFPg0IDtjt7Pg6ukQE+dZE0fyipjw2kKysp0viZPjY5g6aSSd0pvmRtS1NXDgQN9rC9CMqVSCiCw52aMG9/Z2nzdUcn6j+9yrLusRkZ+LyCMi8pSIfIMzgrUC+GM17dbEVe5zlcFZgNfd5ys9aPs4tgbNGGMaARtBqyPL34KP7vWXO4+B62ZBrHcbIhcUl3LTtMVs2uek04+NFl4aP5z+7dM8a6Ox69OnDzExMZSUlLB371727dtn6zCN8Vb5H6SjlZwvP968juv5OdAmoPwJMFFV91fTbk10dZ+za3h9+XWepuwHG0EzxpgGr6ysjL179/rKFqB5ZM0/4IPbcTIoA+2Hwri3Ia7KJRa1UlJaxl1vLGXJdv+6qSevHsJpPVp51kZTEB8fT69e/i/cbRTNmJMqUNXhJ3t4UHd5piSty3pUta2qCtAWuBzoDiwVkWEhtgtO6n5w0vnXxEj3ubL1cUGzAM0YYxq4gwcPUlxcDEBKSortA+WFjZ/Du5OhfKlFRn+44T1ISPWsCVXlVx+u5ou1/uD64Yv6cfHg9p610ZQETnNcuXKlL2mOMcYT5SNblQ3tp1a4rk7rUdW9qvo+TuKSlsD0atqtifk4AeLjIlLlH3v3/OM4geR8D9o+jgVoxhjTwNn0Ro9t+xbeugHKnKCXlj3gxg+gWbqnzTz1xUZmLdzhK992Zncmf6+bp200JT169PBlLz18+DC7d+8Oc4+MaVTWu8+VrTErz6JY2doyr+sBQFW3A2uA/iIS6tSDJ93ngTj7sV1fMVATkRQRuQFnP7jyb4X+HGK7J7AAzRhjGrjMzEzfawvQQrRrMbxxDZS4M1bSOsONH0Kyt+uZZszbxjP/3ugr/3hoB35xfh9P22hqYmNj6du3r69s0xyN8dRX7vNYETkufhCRFOB0nCmC1Y0mzXevO929L7CeKJwRscD2aqJ82kFpLe45gap+ibOnmuBMnZwOHBKRXSKyXkR24ex5Ng0oTx37kKr+J5R2T8YCNGOMaeBs/ZlHslbBzCugyEnWQXJbmPAhpHX0tJnZKzJ5+B+rfeWzerXmT1cOIirKu82um6qK2RzLysqquNoYU1OquhknBX5X4M4Kpx8FkoDpqnqs/KCI9BGR4755UtVcYIZ7/SMV6rnLrf9TVd1SoZ4T3txEJMrdqDoDmKuqIW+CqKp/xEndvwEnUIvCCQB7us9R7vF1wEWq+niobZ6MZXE0xpgGLjBAa9OmTRVXmkod2AgzLoOCI065WUtn5Cy9e9X31dLcTQe4961llC+PGtypOS/cMIzYaPu+1Atdu3YlKSmJY8eOkZuby7Zt2+je3dvfoTFN2B3AXOAZETkPWAuMxtmzbAPwywrXr3WfK3779BBwNnCfiAwBFuLsP3YpsI8TA8Dzgf8Tkf8Cm4GDOJkcz8IZ6coCbgnxZ/NR1dnAbBEZBZyGEzQm4WyuvQ0nGFzoVXsn42mAJiIdgDM5KapTAAAgAElEQVTdR3+gFdDaPb3ffawGvgH+q6o2QdwYY0JQWFhIbq4z4hMTE0N6urfrpJqEw9th+qVwzM3SHJ/mJATJ8HbK4ardR7l1xhKKSp1Rne6tk5gycSTN4uy7Uq9ER0fTv39/Fi50PjutWrXKAjRjPKKqm0VkBPAbnKDpQiATeAZ4VFUP1bCegyIyBvg1cBlwBk7QNQV4WFV3VbjlC+AlnGmUg3FS8B/DCQpnAM/UtO3acIOwOg3EKhPyu4KIJAHXAjcDowJPVbi0JdAH+B5wm3vvQuAV4M3AIVFjjDE1c+TIEd/r1q1bExVlIzG1kpPlBGfZ7veFsUlw/TvQfoinzWw/eIyJUxaSW1gCQNvUBGbcNJr0JO82uzaOgQMH+gK0NWvWcOGFFxITY0GwMV5Q1Z3ApBpeW+m8bTegusd9VFfPKk4cVWvUgv6L5WY1+QXwU5xhv/JfQgmwEtiCs5CuPKJNB1rgDEUOdNsejRPUPSUizwKPq2pNN4czxpgm7+hRfyZim95YS3mHYPplcHirU46Oh+vegM6jPW1mX04B419dyIHcIgBSE2KYNnkUHZonetqOcXTs2JHmzZtz5MgRCgoK2LRpE336WAIWY0zDEVSAJiL3AQ/iBF0CbARmAZ8C36lqYTX3xwNDcTK1jMNJtfkAcKuI/EFVnwqmX8YY09QEjqBlZHibabBRK8iGmZfDfneJRFQMXD0Nup/taTNH84uZ8NoidhzKAyA+JopXJ46kd9uUau40wRIRBg4cyDfffAPAihUrLEAzxjQowc6F+TPOBnPTgBGq2ltVH1HVedUFZwCqWqiq81X1N6raBxju1pVGHewlYIwxjVXgCJoFaDVUnA+zroU9S90DAj9+EXpf4GkzBcWl3DJtMWsznYkh0VHCX8cNY2RXWydY1wKzOW7YsIGCgoIw9sYYY2on2ADtZaCXqk5W1e9C7YSqLlXVyTgjaS+HWp8xxjQFqnrcCJpNcayBkiJ4+0bYPsd/7KKnYOCV3jZTWsZdbyxl4Tb/uvXHrxjE9/vZ76g+ZGRk+P5/KCkpYe3atdXcYYwxkSOoAE1Vb1PVbR73BVXdpqq3e12vMcY0RseOHaOkxEk6kZiYSHJycph7FOHKSuG9W2DjZ/5jP/gtjKjRevcaU1UeeG8lX6z1b3/wywv7cuVwb/dTM1UbNGiQ7/XKlSvD2BNjjKkdS/dljDENVMXpjSK20XGlVOGf98CaD/zHzvx/cPrdnjf1x4/X8e4Sf5bo287qzi1nWqr3+jZgwADf661bt5KTkxPG3hhjTM2FPUATEfvK1xhjgmDTG2tIFT77X1g6w39s9O1wzkOeN/Xi15t58b9bfOWrR3TkgfMtQUU4pKWl0bVrV8AZ1Vy1alV4O2SMMTXkWYAmIrPc1Pu1ued0YLlXfTDGmKbEEoTU0H//DPOe85eHXA8/fAw8HnF8e9FOHvt4na88tl8b/vDjgTayGUaByUJsmqMxpqHwcgTtGmCFiJxV3YUiEi0ivwP+A3T1sA/GGNNk2AhaDSx4Eb76nb/c92K4+BnweEPvj1dm8sB7K3zl0d3Seea6ocREh32iSpPWr18/oqOjAdizZw8HDhwIc4+MMaZ6Xr5zHAM6A/8WkcdFJPZkF4lIL2A+zj5q0cASD/tQ3kZHEXlNRPaISKGIbBORp0WkRQh1nikipSKibnBpjDFhU1JSQnZ2tq/cunXrMPYmQi2bBR//P3+5+zlwxasQHdQWoJX6ZuN+7nlzGWXqlPu3T+XlCSNIiI32tB1Te4mJifTs2dNXtlE0Y0xD4GWANgRY4Nb5c2CBiPQNvEBEfgJ8BwwDFPgDcJqHfUBETsEJ+iYBC4GngC3APcA8EWkZRJ0pOPu05XnYVWOMCdrBgwdRdSKCtLQ0EhISwtyjCLP2I/jwTn+502i49nWIife0me92HOa2GUsoKi0DoHurJKZNHkVqwkm/ozRhUHGaY/n/N8YYE6k8C9BUdTNwOvAoUIoTsC0WkbtEpI2IfAQ8BzQDtgNnqer/qmqJV31wPQ9kAHer6mWq+oCqnosTqPUGfh9EnX/B2UT7Me+6aYwxwdu3b5/vtU1vrGDLf+DdSaClTrnNABj3FsQledrM+qwcJk1ZRF6R0067tARm3DyaVsneBoEmNL169SI+3vmdHDp0iN27d4e5R8YYUzVPJ8erapmqPgqcAWwGEnGCm+3ABYAAM4DBqjqn0oqCJCLdgbHANuCvFU7/Gmca5ngRqfG7tIhcijMadzewx5ueGmNMaPbu9e+xZQlCAuxaDLPGQWmRU07vDuPfh8SgZ7if1I6DeYx/dQFH84udZpLimHHTaDo0T/S0HRO62NhY+vb1T+ixaY7GmEhXJ6uXVXUBzmjafvdQnPv8S1WdoKp1tRnJue7zZ6paVqFPOcAcnBG8U2tSmYhkAC8DH6jqTC87aowxoQgcQbMAzbV3Dcy8AoqPOeXUDnDjh5Ds7X+ffdkF3PDqAvblFAKQHB/DtEmj6JFhu8ZEqsBpjqtWraK0tDSMvTHGmKp5u1LaJSIjgJlAK5xRM9znh0TkoKq+VBft4kxhBNhQyfmNOCNsvYB/16C+l3CC2NuD7ZCIVJYEJUFVWb9+fbBVB82yWDUN9ntu3AKnaeXn54flb0kkic3dTecvbiGmwMlsWRLfnJ1nPEXR3nzY691/m+yCUn7+8W52HHFG6GKjhV+f24a4Y1msX5/lWTuB7P/l0JWVlZGYmEh+fj7Hjh3jm2++oV27duHu1nHs99w0hOv3bGsvGxZPR9DE8RDOSFUvoAgnYchZONMck4AXRORDEamLlGNp7vPRSs6XH29eXUUiMhm4FLhDVfdWd70xxtSX4uJijh1zRolEhJSUlDD3KLyi8w/Q8au7iMl3PviUxiSx6+y/UJTa1dN28orL+OXne9juBmdRAv97dlsGtbVpjZEuKiqKzp07+8rbtm0LX2eMMaYano2giUhnnFGz03FGy1YB16vqSvf8IJx1YTcAFwErRWSyqv7Lqz7UpJvuc5VfI4hIV+Bp4B1VfTuUBlV1eCVtHBORZr179z7Z6XoRzrZN/bHfc+Ozc+dO3+vU1FT69esXxt6EWf5hmDIJct0Rxeh4oq9/i67dzvC0mYLiUia8tpANB5xpjSLw1DVDuHRIB0/bqYr9vxya5ORk30jznj176NatG3FxcdXcVf/s99w01PfvWUSqv8hEDC9H0FbgBGfgJAYZWR6cgbMGTFVvxNnQ+ghOpsV/isjzHvahfIQsrZLzqRWuq8xrQD5whxedMsYYLwWuP0tLq+zPXRNQdAzeuAb2rXbKEg1XTQWPg7OikjLueP07Fmw95Dv2u8sG1GtwZkLXvn17WrZ0dtopKipq8tOCjTGRy8sALRXIAs5X1XtVtfBkF6nqO8BA4EucEa3bPOxD+V/bXpWcL9+tsrI1auWG4QSQ+92NqVVEFJjinv+le+yD0LprjDG1F5jBsXnzamdsN04lRfDWeNi5wH/ssuehz4WeNlNaptz79jK+XOcPih+4oA/Xj+7iaTum7okIgwYN8pWXL18ext4YY0zlvEwS8j5wi6oequ5CVd0DfF9E7iO4fckq85X7PFZEogIzObqbTZ+OMzI2v5p6puNke6yoJ3AmsAxnM+ylIffYGGNqKXAErUkGaGWl8P5tsDkg19P5f4TB13rajKryy/dXMntFpu/Yneecwu1nneJpO6b+DBo0iK++cj4qbN68mdzcXJKTLfumMSayeBagqeoVQdzzpIh85mEfNrv1jQXuBJ4NOP0oTpKSF1X1WPlBEenj3rsuoJ67T1a/iEzECdBmq+r/etVvY4ypKVU9bgStyU1xVIWP/x+sfs9/7KxfwKk/8bgZ5Xez1/LmIv96vwljuvDzsbY+qCFr0aIFnTt3ZseOHagqK1euZMyYMeHuljHGHKdO9kGrDVVd5XGVdwD7gGdE5AMReUxEvgTuxZna+MsK1691H8YYE/Fyc3PJz88HICYmhqSkpDD3qJ795zFY9Iq/PPIWOPtBz5t58vMNvPrtVl/5imEd+fXF/W2hfSMwePBg3+sVK1aEsSfGGHNyYQ/QvKaqm4ERwFRgNHA/cArwDDBGVQ+Gr3fGGBOaiglCmlTAMP9v8PXj/vKAK+GCPzkpFT30/H828eyXm3zl8/u35fErBhIV1YT+Wzdi/fr1Izo6GoDMzMzj/p8yxphIEFSAJiJ3i0i8150RkQQRuSfUelR1p6pOUtV2qhqnql1U9Z6TrY9TVVHVGr3rqupU93qb3miMCYsmmyBkxdvwyS/85R7fh8tegChvv2ecOmcrf/rEn93v7N6teea6ocREN7rvM5usxMTE41Kc2yiaMSbSBPuO8zSwRUTudZNvhERE0kTkfmAr8GSo9RljTGPVJFPsb/gUPghYY9ZxFFw9HWK83cPq7UU7eeSfa3zlMd1b8rcbhhMXY8FZYxOYzXHFihWUlZVVcbUxxtSvYN91puKkof8zsFdE3hGRy0WkxqmQ3KDsKhF5Dyc9/5+AVvhT2RtjjKmgyWVw3DEf3p4AZSVOOaMfjHsL4rxde/eP5Xv4xXv+kZRhnZvzyoQRJMRGe9qOiQw9evQgMTERgOzsbLZv3x7mHhljjF9QWRxVdbKIPAH8EfgRcAVwOaAishFYBGwBDrsPgHSgBc56sJFAD/d4+fTCfwIPqKol7DDGmJMoKytrWgHa3tXwxtVQ4iRFoXkXuOE9aJbuaTOfrc7i3reWoeqU+7dPZcqkUSTFe7kTjYkkMTExDBgwgEWLFgHOnmjdunULc6+MMcYR9LuPqq4GLhaRAcCtwDicIKw3lW8UXa48KDsEzAReduszxhhTicOHD1NS4owkJScnEx/v+VLgyHF4O8y4HAqOOuWk1jD+fUht52kzX63fx51vfEdpmROd9cxIZsZNo0lLjPW0HRN5Bg8e7AvQ1qxZw4UXXkhcnLfTZo0xJhghT6xX1VXuvmEdgAuBx4A5+EfOBH9Adtg995h7bQdV/ZkFZ8YYU73A0bOMjIww9qSO5e6HGZdBbpZTjkuBG/4OLb3dIPrbjQe4bcYSikud4Kxry2a8fvNo0pPsQ3pT0KFDB1q2bAlAUVER69evr+YOY4ypH15uVF0IfOI+ABCRKKClWzyoqrYK1xhjghSYwbHRBmgF2fD6FXBoi1OOjoPrZkG7wVXfV0vztxzk5umLKCpx3pY6tkjkjVtOJSM1wdN2TOQSEQYNGsRXX30FONMcBw4cGOZeGWNMHe+DpqplqrrffVhwZowxIQgcQWvTpk0Ye1JHigvgzXGQudwpSxRc+Rp0O8PTZpZsP8TkqYsoKHbeltqnJTDrllNp3zzR03ZM5AvM5rh582Zyc3PD2BtjjHFY7mBjjGkgGvUIWlkpvHcLbPvGf+yip6HvxZ42s3znESa+toi8olIAMlLief2WU+mU3szTdkzD0KJFCzp37gyAqrJy5cow98gYY0IM0EQkSkSuFJEXROSfIvKRiLwkIuNExFZYG2OMR4qKijh06BDgTM1q3bp1mHvkIVWYfT+s/Yf/2HkPw/AJnjazes9Rxr+6gJxCJ9FKq+Q43rhlNN1aeZuy3zQsgwf7p8/aptXGmEgQdIAmIqcAK4C3cLI4XghcANwEzADWiYhN5jbGGA/s378fdfPAp6enN65sc//5IywJ2ALz1Dvge/d52sTazGxueGUB2QVOcNaiWSwzbx5Nj4wUT9sxDU+/fv2Ijnb2u8vMzDxuKrExxoRDUAGaiCThJAPpiz9LY8VHN+BjEWnhTVeNMabpCpze2KjWny16Bb7+o7888CoY+3sQqfyeWlqflcP1ryzgcF4xAKkJMcy4aTR92qZ61oZpuBITE+ndu7evvGzZsjD2xhhjgh9Buxlnw2mAL4CzgdY4+6CdDnzknmsH3BVC/4wxxtBIA7TVH8Dsn/vLp5wHlz4PUd4tj96wN4dxL8/n0LEiAFLineBsQIc0z9owDd+QIUN8r1esWEFpaWkYe2OMaeqCfRe8FFDg76o6VlX/q6oHVfWIqs5T1UuAqTgjaZd61FdjjGmyAgO0tm3bhrEnHtn6XycpCM60TdoPg6unQ4x3Uzc37XOCs4MBwdn0m0YxuFNzz9owjcMpp5xCcnIyALm5uWzevDnMPTLGNGXBBmj93ec/VXFN+bl+QbZhjDEGJ7tcVlaWr9zgR9Ayl8OscVDqBE607AHXvwPxyZ41sXl/Lte9vIADuU4bSXHRTJ08iqGdbda9OVF0dPRxyUKWLl0axt4YY5q6YAO08ne4jVVcU34uXkQa0Wp2Y4ypX9nZ2RQUFAAQHx9PWloDnp53aCvMvBKKcpxySju44T1IauVZE1v253LdS/PZn1MIQLO4aKZNHsXwLhacmcoFTnNcv349eXl5YeyNMZFJRDqKyGsiskdECkVkm4g8XducEyKS7t63za1nj1tvx5Nc21JEbhaR90Vkk4jki8hREflWRG4SkUa3bViwP1CM+1xc2QWqGjiBO6ay64wxxlSt4voz8TCBRr3K3Q8zL4djbpa8+DS44e/QootnTWw9cIzrXp7PvoDgbOqkUYzomu5ZG6Zxat26NR06dACgrKzM9kQzpgI3g/sSYBKwEHgK2ALcA8wTkZY1rKclMM+9b7Nbz0K33iUi0r3CLVcBLwOjgQXA08DfgQHAK8Db0mDfGE+u0UWcxhjT2DSKBCGFufD6lXBoi1OOjodxb0Kb/lXfVwub9+dyzYvz2JvtBGeJsdG8NnEko7pZcGZqJnAUzaY5GnOC54EM4G5VvUxVH1DVc3ECrN7A72tYzx+AXsBTqnqeW89lOAFbhttOoA3AJUBHVb1eVR9U1clAH2AncAVweag/XCQJNUDrJCKdK3sEcZ0xxpgKGnyAVlIEb4+HTDd9uUTBla9Bl9M8a2KzO62xfOQsMTaaVyeO4NTuNfpC1xgABgwYQEyMM+knKyvruLWfxjRl7qjWWGAb8NcKp38NHAPGu1txVVVPEjDevf7XFU4/59b/w8BRNFX9UlX/qaplgRerahbwN7d4di1+nIgXaoC2BthaxUNrcN2WEPtgjDGNWoPO4FhWBh/eCZu/9B/70RPQ9yLPmti0L5drKwRnUyaN5LRTvFvXZpqGxMRE+vTp4yvbnmjG+JzrPn92kkApB5gDNANOraaeMUAiMMe9L7CeMuAzt3hODftVvtyqpIbXNwihBGiVbVAdzMMYY8xJFBcXc+DAAV+5devWYexNEL54GFa+7S+f9QCMmOxZ9Zv25XBthYQgUyeNtJEzE7SKe6KVlDSqz32maUsQkSUne9Tg3vLd3DdUcr48OWCveqoHEYkBbnSLn1R3fUMSbPKORz3thTHGmJPav38/qs5khPT0dOLj48Pco1qY+xzMfdZfHj4Rzn7As+o37s3hupfn+1LplycEsTVnJhTdu3cnNTWV7Oxs8vLy2LhxI3379g13t4wJt/L0wUcrOV9+vLqNJr2qB+CPOIlC/qWqn9bg+gYjqABNVS1AM8aYetBg15+teAc++6W/3Oci+NGT4FGirfVZOVz/yvwT9jkbadkaTYiioqIYPHgw33zzDeBMc7QAzTQSBao6vI7qLv/jrlVe5VE9InI3cD+wDmdNW6NiWRyNMSaCNcgAbfNX8MFP/OXOY+CKVyAq2pPqV+85yrUvzTsuOJtmwZnxUOA0xw0bNpCbmxvG3hgTEcpHtirbiDO1wnV1Vo+I3An8BSfHxTmqeqiaNhscC9CMMSaCNbgEIZnL4a0boMxdt926D1w3C2ITPal+xa4jjHt5AYfznPqT42OYfpPtc2a81bJlSzp3dpJMqyorVqwIc4+MCbv17nNla8N6us+VrS3zpB4R+RlOtsdVOMFZo0y1agGaMcZEKFU9Ls13xI+gHd4Gr18FRe5oQ0p7ZyPqxBaeVL9k+2Guf3kBR/Od4Cw1IYaZN49meBcLzoz3AkfRli1b5lsLakwT9ZX7PFZEjosfRCQFOB3IB+ZXU89897rT3fsC64nCSeUf2F7g+V/g7Lm2DCc421fbH6KhsADNGGMiVE5ODvn5+QDExcWRllbZjJAIcOwgzLwCct0Rv/g0JzhL6+hJ9Qu2HOTGVxeQU+hk1GveLJY3bjmVIZ1qso7cmNrr378/sbGxAOzbt4/MzMww98iY8FHVzTgp8LsCd1Y4/SiQBExX1WPlB0Wkj4j0CbxQVXOBGe71j1So5y63/k9V9bhtuETkVzhJQZYA56nqARqxYLM4GmOMqWMV159FRUXod2pFeTDrGji4ySlHx8F1b0Cbfp5UP3fTAW6atpj84lIAWibFMfPm0fRtl1rNncYELz4+nn79+rF8+XIAvvvuO9q3bx/mXhkTVncAc4FnROQ8YC0wGmfPsg3ALytcv9Z9rpgd6iGcjaXvE5EhwEKgL3ApsI8KAaCITAB+A5QC3wB3y4kJp7ap6tQgf66IYwGaMcZEqAaRIKS0BN6dBLsWuQcELn8Zun7Pk+r/s34ft81YQmGJsy9q65R43rh5ND3bpFRzpzGhGzp0qC9AW7FiBWPHjiUuLi7MvTImPFR1s4iMwAmWzgcuBDKBZ4BHa5qsQ1UPisgY4NfAZcAZwEFgCvCwqu6qcEs39zka+Fkl1X4NTK35TxPZLEAzxpgIFfEBmirMvg82BOwPesHj0P8yT6r/ZFUmP521lOJSZ+1P29QE3rhlNN1bJ3tSvzHV6dKlCy1btuTgwYMUFRWxevVqhg4dGu5uGRM2qroTmFTDayvdV8UN5u5xH9XV8wgnTods1CJ0vowxxpiIz+D49Z/gu2n+8uk/g9G3eVL1+0t3cecb/uCsQ/NE3rrtVAvOTL0SEYYNG+YrL1myJIy9McY0FRagGWNMBCopKeHAAf8a6IyMjDD25iS+mwH/+YO/POga+P4jnlT9xoId3Pf2ckrLnOCse6sk3rl9DF1aJnlSvzG1MWTIEN/6z127dh33xYkxxtQFC9CMMSYC7d+/n7IyZ91VixYtiI+PD3OPAmz8HP4ZMCul+9lwyXNw4qLtWnvlmy089P5KyjOa926Twlu3jaF9c2/2UTOmtpKSkujbt6+vbKNoxpi6ZgGaMcZEoIhdf7b7O3h7AqiTUZG2A+HqGRATWuIEVeWZf2/kd7PX+o4N6pjGm7eeSuuUCApOTZM0fPhw3+sVK1ZQXFwcxt4YYxo7C9CMMSYCRWSAdmgrvHE1FLvb3KR1gnHvQEJo6e5Vlcc+XseTn2/wHRvZtQWv3zyaFkmWMc+EX9euXWnRwtlwvaCggDVr1oS5R8aYxswCNGOMiUARF6AdO+BsRH1sv1NOaO5sRJ3aLqRqS8uUB99byUv/9e9JekbPVkybPIqUhNiQ6jbGK1FRUZYsxBhTbyxAM8aYCKOqZGVl+cphz+BYlAezroVDm51ydDyMewta9w6p2sKSUu6etZQ3F+30HRvbrw0v3ziCZnG2C4yJLIHJQnbs2MH+/fvD3CNjTGNlAZoxxkSY3Nxc8vLyAIiLi6N58+bh60xZKfz95uM3or7iFeh8akjV5hWVcPO0xcxemek7dsWwjjx//TASYqNDqtuYupCSkkLv3v4vJWwUzRhTVyxAM8aYCBM4vTEjI8P3rX29U4VPHoD1s/3HLngc+l0SUrVH84sZ/+pCvtno30Zg0uld+b8rBxETbW9LJnIFTnNcvny5JQsxxtQJeyc0xpgIEzHrz+Y+Cwtf8pdP+2nIG1Hvzynk2pfms2T7Yd+xn32/Jw9f1I+oqNDT9BtTl0455RTS0tIAyM/PZ926dWHukTGmMbIAzRhjIkxEBGgr34XPf+Uv978cvv+bkKrccTCPK/82l7WZ2b5jD1/Uj599vxfiwR5qxtQ1SxZijKkPFqAZY0yECQzQwpIgZNu38MFP/OUup8NlL0AIUy1X7znK5S/MZftBZ21dlMATVw1m8ve6hdpbY+rV0KFDfV8obNu2jYMHD4a5R8aYxsYCNGOMiSDFxcXHZYfLyMio3w7sWwdvjoPSIqfcqjdcMxNiE4Kuct7mg1z74nwO5BYCEB8TxYvjR3DF8I5e9NiYepWamkrPnj19ZRtFM8Z4zQI0Y4yJIFlZWZSVlQGQnp5OQkLwgVGt5WTB61dBwVGnnNwGbngXmqUHXeUnqzKZMGUhOYUlAKQkxDDjptH8oF8E7O1mTJCGDx/ue7106VJLFmKM8ZQFaMYYE0F27vTvCdapU6f6a7gwF964Go7ucMqxSTDubWjeOegqZy3cwR2vf0dRiRNwZqTE8/ZtYxjVLfiAz5hI0LNnT9/2F/n5+axatSrMPTLGNCYWoBljTATZtWuX73XHjvU0BbC0BN6dBJnLnbJEw9XTof2QoKpTVZ7990YefG8lZeoc69Yqib//5DT6tkv1qNPGhE9UVBQjR470lRcsWICqhrFHxpjGxAI0Y4yJIPUeoKnCv34OGz/zH7voKej5/aCqKykt46H3V/HE5xt8xwZ2SOOd28fQKb1ZqL01JmIMHTqUmJgYwJmaHDj6bYwxobAAzRhjIsTRo0fJznZS0MfGxtZPgpA5T8OSKf7yGT+H4ROCqiq/qJTbZy5h1sIdvmOn92jJrFtPpVVyfKg9NSaiNGvWjIEDB/rKCxcuDGNvjDGNiQVoxhgTIQJHzzp06EB0dHTdNrjyXfjiEX950DVw7v8GVdWhY0Vc9/J8vli7z3fssiHtmTJxFMnxMSF21JjINGrUKN/rNWvWkJOTE8beGGMaCwvQjDEmQtTr9MZtc47f66zrGXDJcxDEhtE7DuZxxQtzWbbziO/YbWd158mrhxAXY28zpvFq166dL5lPWVmZpdw3xnjC3jmNMSZC1FuAtn/D8Xudte4D18yAmLhaV7Vyl7MB9dYDxwAnvnvk4n48eEFfoqJqH+wZ09AEjqItXryY0tLSMPbGGNMYWIBmjDERoKSkhD179vjKdRag5e6D16+AAh1WYy8AACAASURBVHe0K7kNXP8OJLaodVX/XruXq1+c59uAOi4miufHDWPi6d287LExEa1v374kJycDkJuby9q1a8PcI2NMQ2cBmjHGRICsrCzfN+8tWrTwfeDzVFEezLoWjpTvddYMxr0V1F5nM+Zt45bpi8kvdvqclhjL6zeP5oKB7TzssDGRLyYm5riNqy1ZiDEmVBagGWNMBKjz6Y1lpfDeLbDbXSMjUXDlFGg/tHbVlCm/+2gNv/pwtW+Ps44tEvn7T8YwsqttQG2apuHDhxMV5Xyk2rFjB1lZWWHukTGmIbMAzRhjIkCdB2if/QrWfeQvX/An6H1+rarILyrljte/45Vvt/qODe7UnPfvOJ0eGSle9dSYBic1NZW+ffv6yjaKZowJhQVoxhgTAQI3uS3PCueZBS/C/L/6y2PuglG31KqKA7mFXPfyfD5Z7R8ZGNuvDW/eciqtU2yPM2NGjx7te71ixQry8vLC2BtjTENmAZoxxoRZTk4OR48eBZz1LG3atPGu8vUfwycP+Mt9L4Yf/LZWVWzcm8OPn59zXBr9yad344UbhpMYV8d7tRnTQHTq1Im2bdsCTtKfZcuWhblHxpiGygI0Y4wJs8Dpje3bt/dug+o9S+HdyaBlTrnDCPjxSxBV8z/9X2/Yz+XPz2XnoXwAotw0+g9f3I9oS6NvjI+IHJdyf8GCBZZy3xgTFAvQjDEmzAKnN3q2/uzITnjjGih2p1k17wLXvQlxzWpcxYx525g8dRE5hSUANIuL5sXxIyyNvjGVGDBgAM2aOf+PHT16lDVr1oS5R8aYhsgCNGOMCbPAETRP1p8VZMMbV0PuXqec0ByufxeSW9fo9pLSMh75x2p+9eFqSt1Uje3SEnjn9jH8oJ+H0y+NaWTi4uKOG0WbM2cOqhrGHhljGiIL0IwxJoxKS0u93aC6tBjemQD73G/uo2LhmpnQuleNbs8uKOamaYuZOneb79jgjml8eOfp9G+fFlrfjGkCRo4cSUxMDODsb7hly5Yw98gY09BYgGaMMWG0d+9eSkqcKYRpaWmkpISQrl4V/vU/sPlL/7FLnoVuZ9To9h0H87jyhbl8vWG/79iPBrbjzVvHkJGaEHy/jGlCkpKSGDrUv7/g3Llzw9gbY0xDZAGaMcaEkafp9ec+A0um+MtnPQBDrqvZrZsOcMlfv2XD3lzfsZ+e24NnrxtqmRqNqaUxY8Yg4iTR2bx5s21cbYypFQvQjDEmjDzboHr1B/D5w/7yoGvg7Acqv96lqkyft43xry3kSF4xAHExUTx1zWDuH9ubKMvUaEytpaenH7dx9Zw5c8LYG2NMQ2MBmjHGhJEnAdquxfD+bf+fvfuOj/I6E77/OzPqvSGJJgmJIokOAiHJYIqL3CgxXhtjxyWO144dZ1OefXaz2bR3s+/z5tlNceJk4yQ4cVyIY4MhBgMGTBMCJDBFgARIQogiBOq9zJz3j3s0SEICIY00I+n6fj7zuedu5z7DjWbmmnPOdW6sR6cZXRvVrYOr5lYr311/gu+3SwYS7u/JX1+cx4qZDsomKcQwlZaWZn+ek5NDZWXlLY4WQogbhmSAppQao5Rao5S6rJRqUkqdV0r9QikV3MPzfZVSq5VS7ymlcpVSdUqpGqVUtlLq20opj/5+DUKIoa+2tpaKigoAzGazfZLbO+FWexnefwJaG40NoeONpCBunrc873ptE6v/cID3D93oYjltTCAbX72LmVE9eqsUQtzC6NGjiYmJAYyW6gMHDji3QkKIQWPIBWhKqTjgMPAccAj4OVAAfAPIVEqF9qCY+cA7wP1ADvAr4H1gNPBfwOdKKRkxL4Tok84TVLdlfuspU3MtY3Z/E+psST28Q+DJD8An5Jbn5VyqYtmvM8g6X2HftnzGKD74xxQiA+WtTQhHad+KdvjwYRoaGpxYGyHEYDHkAjTgN0A48JrWernW+l+01osxArVJwE96UEYJ8BQwUmu90lbGi8BE4AiQCrzSP9UXQgwXfereaGlhVMa/4lldaKybPeCJ9yA07panrTtykUd/u59LlcYXRaXgXx6I5+ePz8DLXZKBCOFI48ePJzw8HICWlhays7OdXCMhxGAwpAI0pVQscB9wHnij0+4fAHXA00op31uVo7U+qrV+V2vd3Gl7DfDfttWFjqizEGL46nWApjVs/g6+JQdvbFv2BkSndHtKi23y6W99cIymVisA/p5u/PGZJF66O86ecU4I4ThKKVJTU+3rBw8epKWlxYk1EkIMBkMqQAMW25bbtNbW9jtswVUG4APM68M12t5ZW/tQhhBimLNYLFy6dMm+fkcBWuav4fCfbqwv/FeY9g/dHn6tponVfzjYYfLp8eF+fPxqGovjI+6g1kKIOzVlyhT7/Ia1tbUcP37cyTUSovf6muehXTkhtvPO28q5bCu3yw9DpdRKpdSvlFJ7lVLVSimtlHrHMa/K9dzZgAfXN8m2PNPN/rMYLWwTgR29vMbztuWWnhyslDrczS4vrTV5eXm9rEbvXb9+fcCvKQae3GfXVlZWZv8l3dvbm5KSkh7NleR3cRej9v47be1dpZGLqIhcDt28l+Rda+THO0u4Xn/jN6W0aF++Mz+c1vJL5JX3+aWIfiZ/y4NfXFwcR48eBWDXrl34+PhgMnX8jVzu8/DgrPuste5zGbY8D/sxhhJtAHKBuRh5HtKVUmla67IelBNqK2cisBNYC8Rj5I94SCmVorUu6HTa94DpQC1w0Xb8kDXUWtACbcuqbva3bQ/qTeFKqVeBdOAosKY3ZQghBNAhGIuI6FkrlmfZKUbu/3cUxgdtVdBkzk3+py7T6Wut2ZxXxbc/vWQPzhTw3OwQ/n1RJD7uQ+3tXwjXNX78eNzd3QGoqamhqKjIyTUSolcckecB4D8xgrOfa62X2MpZjhHohduu09k3becEAC/38XW4vKHWgnY7bd9i7vhnBKXUl4BfYCQQeVRr3aNO5Frr2d2UV6eU8pk0aVJXuweEM68tBo7cZ9e0f/9++/OZM2fe/j5VnIeN/wyWJmM9eBzXFv2cUM+gm85taLbwvY9z+OjINfu2AC83Xl81k4WTwh31EsQAk7/lwe369evs2rULgDNnznDvvfdiNt+cmEfu8/Aw0Pe5r+OMe5Dn4UWMPA/f1lrX3aIcX+BpjLwQP+i0+9cYgdj9SqnY9q1oWuvP25XRh1cyOAy1n1DbWsgCu9kf0Om4HlFKLcdofi0FFnbR7CqEED3W1NREcfGN+cdiY2NvfUJ9ObyzEupKjXWvQFj9NyyeN3cGKLxex4rfZPDRkRsJSOIj/fn71++S4EwIJ5o3bx5eXsY0FuXl5Zw4ccLJNRLDkJdS6nBXjx6c66g8DymAN5BhO699OVZgm211UQ/qNGQNtQCtbRDGxG72T7AtuxujdhOl1GPA34CrwN1a64EfNCaEGFLOnz+P1Wp8vkVERNgTCHSppcGYiLrsrLFu9oBVayFswk2Hbsm5wtJf7SO35MZn3qOzxrD+a2lEh94yea0Qop95eXl1yOi4e/duLBaLE2skxB3pSZ4H6P47uKPLGdKGWhfHtubP+5RSpvYRvlLKH0gDGoADPSlMKfUk8DZwCVgkLWdCCEfIz8+3P4+Lu8W8ZVYLfPQCFLdLp/+lNyE6tcNhLRYr/3drHm/uufEW5eFm4kdLJ/PEnLHDojuIEINBcnIymZmZNDQ0UFFRwbFjx5g1a5azqyWGj8buht70gKPyPPRrvoihYki1oGmt8zGaRmO4eSLpHwG+wNvt+8YqpeKVUjdlglFKPQP8BbgALJDgTAjhKD0K0LSGLf8KuZ/c2Hb/f8LkFR0OK61t4Yk3D3QIzsYEe7Pu5VRWzY2S4EwIF+Lp6XlTK1prq8zaI4aEXud56KdyBrWh1oIG8DWM1J2vK6WWAKeBZIy+rGeAf+t0/Gnb0v4tRim1CCNLowmjVe65Lr7kVGqtf+Hw2gshhrTKykrKyowsxG5ubkRFRXV94P5fwaHf3Vif9wqkdPzd6UBxHf+19yo1TTeGAyyJD+dn/zCDQB93h9ddCNF3c+fOJTMzk/r6eqqqqjh69ChJSUnOrpYQt+OoPA/9ki9iqBlyAZrWOl8plQT8GCMl/oPAFeB14Eda657M+hPNjdbF57s5pggjq6MQQvRY+9az6Ohoe+rtDk58CJ/9+431xOVw33/YV5tbrfx0Sy5/2HfFvs1sUnz7vom8tCAOk0lazYRwVZ6enqSlpfHZZ58BsGfPHmbMmOHkWglxW47K8+DwfBFD0ZAL0AC01sUYk9315Nibvslorf8E/MmxtRJCiB50b8z7FNb/4431qFRY8TuwTWpbXF7P19//gqPFlfZDRgZ68fqqmcyJCem3egshHGfOnDns37+furo6qqurOXLkCIGB3TUoCOESHJXn4YDtuDSllH/7TI5KKRNGKv/21xuWhtQYNCGEcGVWq5WCghtjxW4K0M5thw++DFbbmJSwSfDEu+BupObeklPCQ6/v7RCczR3jw6bX5ktwJsQg4uHhwV133WVf37t3r2R0FC7NUXketNa1GDkefIEfdirnVVv5W4d77och2YImhBCu6PLlyzQ2NgLg5+dHeHi7eckK98Da1WBpNtaDx8GXPwafEBqaLfw/m07x3sEL9sPdTIpnZ4Xw6JQgQnw9BvJlCCEcICkpiYyMDGpra6mpqSE/P5+JE4d1ZnHh+vqc58Hmu8BC4FtKqRnAISABWIYx53DnALBtTuLlttVI2zJFKfUn2/PrWuvv9OpVuSAJ0IQQYoB07t5oTz5UlAnvPQ6tRvBGYBQ883cIGMWpy9V8/f0j5F+z/yjJ6CBvXl81E7/G0oGsvhDCgdzd3bnrrrvYsmULACdPnmTcuHFOrpUQ3XNQnge01mVKqRTgBxhB13ygDHgL+L7W+mIXp80Anum0Ldb2ACM3xJAJ0KSLoxBCDJAux59dPAzvPgYt9ca6/yh4ZgM6cAxr9hWy/I2MDsHZg1Mj2fzafGZHBw9k1YUQ/WD27Nn2ieobGxs5ffr0bc4Qwrm01sVa6+e01iO11h5a62it9Te6Cs601qqrXA+2feW286Jt5YzUWj/fTXCG1vqHbeV184hx8Et1KgnQhBBiADQ2NnLx4o3PndjYWLhyDN5ZAc22MdK+4fDMRq65j+a5P2Xx409O0WwxxmF7u5v56aPTeOPJWZJCX4ghwt3dnSVLltjXT58+TUVFhRNrJIRwBRKgCSHEADh//jxWqxFsRUZG4leVB28vg0bbVC8+ofDMRj4rDSD9F3vYlXfNfu6U0QF88tpd/MOcsTLxtBBDzLRp0xg1ahRgJBLatm2bk2skhHA2CdCEEGIAdOjeGOYJf14KDbZfyr0CqX/iI/73nha++nY2ZXXN9mNfXBDLRy+nEjfCb6CrLIQYACaTiQceeMC+fvr06Q7ZXoUQw48EaEIIMQA6pNc/9StorjVWvEM4dc9fSF9byV+zi+3HhPt78vbzc/nugwl4upkHurpCiAE0duxYYmJi7OtbtmyRtPtCDGMSoAkhRD+rqKigrKwMADdaGGs9D4D2i2TNxDd4+KNaLpTX249/aNpItn1zAQsmjnBGdYUQTjB9+nTc3Izk2qWlpRw+fNjJNRJCOIsEaEII0c/at57FcBF3LDT7R/EV03/w44Maqzb2+Xu58csnZvDrVTMJ8pG5zYQYTnx8fEhMTLSvf/7559TX19/iDCHEUCUBmhBC9LP8g1vsz+MooswnlsXl/5udpT727alxoWz9pwUsmzFaEoEIMUzFx8cTFBQEQENDA7t27XJuhYQQTiEBmhBC9BerBeumf6agtMa+yc2kuaf8n7loMeYx83Qz8b2HEnjnK8mMCvJ2Vk2FEC7AbDZz//3329ezsrK4evWqE2skhHAGCdCEEKI/NNXC2ie5lLWRRrwA8NSNPFf/ChUEADAzKojN35jPC/NjMZmk1UwIYbSijRs3DgCtNVu2bEFr7eRaCSEGkgRoQgjhaNWX4a10OLOFk0ywbz5lGUUtvni4mfjug/F8+JKkzxdCdKSUIj093d7VubCwkGPHjjm5VkKIgSQBmhBCONKV4/D7JVByAitwkkn2XfnWMGaMDWLza/N5cUEcZmk1E0J0ISIigjlz5tjXP/30UyorK51YIyHEQJIATQghHOXMVliTDjWXASjUY6nBaCFr1G48fe8cPno5lfHh0momhLi1JUuWEBxsjFVtampiw4YNWK1WJ9dKCDEQJEATQoi+0hr2/Rz9/hPQUgdAtfbm19bH7YdMmzqZlxdNkFYzIUSPeHp6smLFig5dHQ8dOuTkWgkhBoIEaEII0ReN1ei/PgXbf4jSxq/bF3UYK5t/iFe7YCxtzixn1VAIMUhFRUWRlpZmX9++fTvXrl1zYo2EEANBAjQhhOit0lxa/mchKvcT+6Zs60RWNP2YidFReKpWAAICAhg7dqyzaimEGMQWLlxIREQEAK2traxfvx6LxeLkWgkh+pMEaEII0Qstxz+k+X8W4l6Zb9/2Vuv9vOr+Y3745GKWRDTZt0+ePBmTSd5uhRB3zs3NjRUrVmA2mwG4fPkye/fudXKthBD9Sb4xCCHEnbC0cPmv38J93VfwsDYA0KA9+KeWr1E45/ts/c493JcQRm5urv2UKVOmOKu2QoghIDIykkWLFtnXd+/ezaVLl5xYIyFEf3JzdgWEGAgWi4XKykpqamqoqamhurra/ry2thaLxYLVar1p6enpiZeXF97e3nh7e9ufBwYGEhYWRlhYGJ6ens5+eWKAXCvKpe79Z4lpPG3fdt4awX8Ff4+vrlzK9LFBAJw+fZqmJqMFLTg4mFGjRjmlvkKIoSM1NZW8vDyKi4vRWrN+/XpefPFFPDw8nF01IYSDSYAmhpz6+npKSkq4evWqfXnt2rV+67MfEBBgD9YiIiKIjo4mNDTUnnlLDH5NLa3s+/B15uX+f4xQjfbtn+vZXFn8c365YFqH7Iw5OTn251OnTpX/C0KIPjOZTKxYsYLf/va3tLS0cP36dT766CMef/xx6UItxBAjAZoY9Gpqajh//jyFhYUUFhZSUVExoNevrq6murqagoIC+zY/Pz+io6OJiYkhOjqaESNGyJf0QWrv8bO0bvwGS1ozwHYLW7SZTSO+QsrTP2JRoE+H45uamsjLy7OvS/dGIYSjhISE8MADD7Bx40YA8vLy2Lp1Kw888ICTayaEcCQJ0MSg09LSQn5+PgUFBRQWFvY45bC/vz+BgYEEBATg7++Pv78/AQEB+Pn54ebmhtlsxmQy2ZdKKZqbm2loaKChoYHGxkYaGhqor6+nvLyc69evU15e3uXEobW1tZw8eZKTJ08CRsCWkJBAYmIi0dHR8mvnIHD+eh1//XAtT135CaNVmX17sWk0Fem/YfnchV2el5eXR2urkb0xPDyc8PDwgaiuEGKYmDVrFteuXSMzMxOAgwcPEhQUREpKipNrJoRwFAnQxKDQ2NjI2bNnOX36NGfPnqWlpaXbY81mM+Hh4URERBAZGUlERAQRERH4+Ph0e05vWSwWKioquH79OteuXaO4uJiioiL7+KM2tbW1ZGVlkZWVha+vLwkJCUyePFmCNRdUVd/Cbz47wYjs/+Z/mTZhUtq+L2/0l4h76nXGevt3e3777o3SeiaE6A/33nsvVVVVnDp1CoCtW7cSGBhIYmKik2t2g9aa3NxcsrKyaG5uJiIigpEjRzJy5EjCw8Nxd3d3dhWFcFkSoAmX1dTUxOnTpzl16hT5+fndjiEzm82MGTOGcePGMW7cOEaPHo2b28D81zabzfbxZ/Hx8QBYrVauXr3K+fPnKSoqoqioiIaGBvs5dXV1ZGdnk52dja+vLzNnziQpKYmgoKABqbPoWovFyrsHiti7/WO+Z/kt48xX7fvqzAFYHv4lk2Z+6ZZl1NfXc+7cOfu6BGhCiP7QNh6turqaixcvArBu3Tr8/f2dPuei1pr8/Hx27tzJ5cuX7dvb6glG/UeMGEF0dDTz58/H37/7H72EGI4kQBMuRWtNUVERX3zxBadOneq2pSw0NJT4+HhiY2MZO3asS2WxMplM9l8JU1JSsFqtFBUVcerUKU6dOkVdXZ392Lq6Ovbt20dGRgYTJ05kzpw5xMbGSqvaANJaszO3lJ9vOswTlX/gj247OkxAUjPqLvyf+D0E3D4TY25urr3L6+jRowkJCemvagshhjl3d3dWrVrFH//4R8rLy2ltbeX999/nhRdecNp7T1FRETt27ODChQu3PK7th8yrV6+Sk5PDI488QkJCwgDVUgjXJwGacAmVlZUcO3aMo0ePdpvkIzIykoSEBBISEgbVuB6TyWRv3XvggQe4cOECJ0+e7BCsaa3Jy8sjLy+PkJAQkpKSmDVrFl5eXk6u/dB2rLiS//NpLp7nd/A79z8y2u3GWLMWNz/cHvhP/Gd9GXqY4OXEiRP259J6JoTob76+vqxevZo//OEP9jHS77zzDs8999yAtkpVVFSwadOmDj0IwJhku+2Hx5KSEkpKSrhy5Qrl5eX2Y+rr6/nrX//KjBkzSE9Pl889IZAATThRWzeIQ4cOcebMmS6PGTFiBNOnTycxMXFItEaYTCZiYmKIiYkhPT2dM2fOkJWV1SEDZHl5Odu2bWPPnj0kJyczb948vL29nVjroafweh3/tTWP7BMn+Tf3d1nqkdlhv2XiA7g//LMetZq1acsm2mby5MmOqq4QQnQrNDSUVatW8ec//xmLxUJ5eTlvvvkmTzzxBKNHj+7361+8eJH33nuP+vp6+zaTycSsWbNYsGABAQEBAEyYMMG+v7GxkcLCQj799FOqq6sBOHr0KIWFhaxYsYKYmJh+r7cQrkwCNDHgmpqaOHr0KIcOHaKsrOym/V5eXkyZMoWZM2cyatSoIZue3mw221sEr1+/TnZ2Nl988YU9wUhjYyO7d+8mMzOT5ORkUlJS+iXRyXBSWt3IL3ec5aOsQp5Vm/ip53p81Y2ELlbvUEwP/hTzlEd73GrW5sSJE2htJBSJjo62fykRQoj+FhUVxaOPPsrf/vY3tNbU1NSwZs0ali5dyvTp0/vtuqdOnWLdunX2zLVKKaZNm8bdd999yx9Vvby8SEhIICYmhs2bN9t7H1RVVfGnP/2J1NRUFi9ePGDjyYVwNfI/XwyYsrIyDh48yNGjR2lubr5pf2xsLDNnziQ+Pn7YZXcKCwsjPT2dxYsXc+LECTIyMuxdQJqbm9m7dy8HDhxg7ty5pKam4uvr6+QaDy6V9c38fm8Ba/adZ47lCJvc3ibOdKXjQVMfw5T+f8A37I7Lt1gsHDx40L4+bdq0vlZZCCHuSGJiIqtXr+bDDz+ksbERi8XC+vXruXLlCvfeey9ms9lh19Jak5mZybZt2+zbvL29WbVqFVFRUT0ux9vbm0cffZRJkybxySef0NjYCMD+/fu5evUqTzzxxLD7PiAESIAmBsDFixfZv3+/PR1wex4eHsycOZM5c+YQFnbnX4yHGg8PD2bPns2MGTM4efIke/bs4fr164Ax/1tGRgZZWVksWLCA5ORk+eC6jerGFtbsK+SPewsJbL7ML9ze4X6P7I4HhSfCAz+FcfN7fZ3Tp09TVVUFgI+PjwRoQginGD9+PF/96ldZu3atfY7QAwcOUFpaysqVKx3SC8NisbBlyxaysrLs20JCQli9ejWhoaG9KnPKlClERUWxYcMG8vPzAcjPz2ft2rUSpIlhSQI00S+01pw9e5aMjAyKiopu2h8WFsbcuXOZPn06np6eTqihazObzUybNo0pU6Zw6tQp9uzZQ2lpKWC0qG3fvp2srCzuuecepkyZMmS7gfZWXVMrf9p/njf3FGBqKOOf3DbwlMdneKpW+zHaMwC16Lsw5wUw9/7DX2vN/v377etz5syRLxNCCKcJDQ3lhRdeYN26deTl5QFQUFDA73//e+69917i4+N7nSm4sbGRdevWdRg3PnbsWFatWtXn4C8gIICnnnqKXbt2sXv3bkCCNDF8SYAmHMpisZCTk0NGRoY9oGgvLi6O1NRUYmNjJajoAZPJxJQpU0hMTCQ3N5edO3faW9Sqqqr46KOPOHDgAPfddx/R0dFOrq3z1TW18u7BIn63u4C6uhqeN2/hJc+NBKiGjgfOWI2654fg1/dsoBcuXLDP9WM2m5kzZ06fyxRCiL7w9PTk8ccfZ/fu3fZgp6Kigg8++ICgoCDmzp17R5mCL1++zOHDhzlx4kSHIQpTpkxh2bJlDguelFIsWrQIQII0MaxJgCYcorW1laNHj7Jv3z4qKys77GsLMlJTU4mMjHRSDQc3k8lEYmIikyZN4vDhw+zatcueMevSpUu89dZbJCYmkp6ePiyTU1Q3tvD2/vP8cV8h1fWNrDTv4ZueHxKpOk3ZMGYu3P8TGDvXYdfOzLyRAXL69On4+fk5rGwhhOgtk8nEokWLiIyMZP369fbAqrKykm3btrFr1y5mzJjBnDlzCAoKws3NrcMPp83NzeTk5JCdnd1hwuk2d911F4sXL+6XeTslSBPDnQRook+am5s5fPgw+/fvp6ampsM+d3d3Zs+ezbx58wgKCnJSDYcWs9nM3LlzmTZtmj1xiMViAYxsWufOnWPRokXMneu4AMSVVdQ181ZGIW/tP099YxMPmzJ5zWP9zQlAQifAPT+A+IfvODvjrZSVlZGbm2tfnzdvnsPKFkIIR0hISGDMmDEcOnSI7OxsGhqMHgXNzc0cOnSIQ4cO2Y91c3PD3d0dNzc3mpqaukzoNWLECBYsWMDUqVP7td4SpInhTAI00SuNjY1kZWWRmZnZYe4TMLIyzZs3j7lz58r8Xf3Ey8uLe++9l6SkJHbs2EFOTg5gfOBu3bqVY8eOMXXq1CGbeKWkqpE1GYW8c6CIpuZmlpsyeMXjY2JNJR0P9IuAhf8KM58Gs+Pf7g4cOGB/Pn78+EE1gboQYvjwnRgO/AAAIABJREFU9/dnyZIlLFiwgOPHj3PgwAF7EpH2Wltb7Snz2zObzSQmJpKUlERUVNSADVHoKkj729/+xuOPP+7QrJRCuBoJ0MQdaWho4ODBgxw4cMCeDreNn58fqampzJ49WxJ/DJDg4GBWrlxJUlISn3zyiX18WklJCSUlJYwfP56oqKghEyifvVrDm3sK+PjoJbSlhRXmfbzq8THRpk7jHT0DIPU1SPkaePTPlAT19fUcPXrUvp6amtov1xFCCEdp69kya9YsCgoKOHDgAMXFxTQ3N2O1Wm86PiQkhKSkJKZPn+606V06B2lnzpxh8+bNPPzwwzKWXQxZEqCJHqmvryczM5NDhw7ZJ1JuExgYSFpaGjNnzpRuB04SExPDSy+9RGZmJrt377b/Anru3Dl+/etf89BDD5GYmOjkWvaO1pqs8xX8bnc+O3JL8aWBp827eN7zU8ao6x0P9gqEeV+D5JfAu3+71R4+fJiWlhYAIiIiGDduXL9eTwghHEUpRVxcHHFxcfZtVquV1tZWWlpa7J8hAQEBLhEELVq0iNbWVjIyMgDj/TcoKIj583s/PYoQrkwCNHFLtbW19sCs7ctom+DgYObPn8/06dOlq4ELcHNzY/78+UyZMoXNmzdz9uxZAOrq6vjggw9ITEzkwQcfHDRJLFosVj7NKWHNvkKOFlcSQTn/4raVJ807CFAdu9XiFQQpr0Lyi0aQ1s9aW1s7TEydkpLiEl9ihBCit0wmEx4eHnh4eDi7Kl1asmQJ1dXVnDhxAoAdO3YQEBDA9OnTnVwzIRxPAjTRpaqqKjIyMjhy5MhN/dHDwsLsgYAEZq4nODiYJ598kh07dnD48GH7gPBTp05RWFjIgw8+6NJzp5XXNfP+oQv8JbOIkupGEtV5/tt9M0tNmbgrS8eDvUMg9VWY81XwGrjslTk5OdTW1gJG194pU6YM2LWFEGI4MplMLFu2jJqaGs6fPw/Ahg0b8Pf3JzY21rmVE8LBJEATHZSVlbFv3z6OHTt2U3/08PBwFixYQGJiYr+k1RWOo5Ri7NixREREUFBQwBdffAEYYwg/+ugjcnJyePjhh/H393dyTW/IK6nhrYxC1n9xCd3axAOmgzztsZ0k05mbDw6Jg5RXYPoq8Ojb5Kh3SmvdIbV+cnIybm7yViqEEP3Nzc2Nxx9/nDVr1nDt2jWsVit//etfef7554mIiHB29YYFpdQY4MdAOhAKXAE+Bn6kta641bmdygkBvg8sB0YCZcAW4Pta64v9ee3BQL5VCMBIKpGRkUFOTg5a6w77Ro4cyYIFC5g0aZIEZoOMh4cHy5YtY/Lkyfz973+nqqoKgLy8PIqKinjwwQeZOnWq01rTmlotbMkp4d2DFzhUWM4YVco/mXfwD567CFU1N58QlQqpX4eJ6eCk/4sFBQVcvXoVuDHgXgghxMDw9vbmqaee4g9/+AM1NTU0NTXx7rvv8pWvfIXAwP7v4j6cKaXigP1AOLAByAXmAt8A0pVSaVrrsh6UE2orZyKwE1gLxAPPAQ8ppVK01gX9ce3BQgK0YUxrTUFBAfv37yc/P/+m/VFRUSxYsIC4uDiX7Q4nemb8+PG8/PLLbN++nezsbMCYKmHdunXk5uby0EMPDWiGruLyet47dIEPsoqpqatjsekL3nL/nLtNxzGpjj8QYHKHxKUw7xUY49xgyGq1sn37dvv6zJkz8fEZ2BY8IYQY7gIDA1m9ejVr1qyhubmZ6upq3n33XZ577rkhk7XYRf0GI0B6TWv9q7aNSqmfAd8EfgK81INy/hMjOPu51vpb7cp5Dfil7Trp/XTtQUF1bi0RA0MpVeft7e3TeQ6xgXD69GkuXLhAYWEhJSUlN+2Pi4tj/vz5xMTEDHjdhOPk5eUBMGnSpA7bCwsL2bBhA5WVlfZtvr6+LF269KZjHam51crO3KuszSpm95lSJlPISvMelpn3E6xqbz4hcCzMfhZmfRn8XGN+saysLDZt2gQYXW1eeeUVgoODnVaf7u6xGFrkPg8Pcp/vXH5+Pu+++659SEZMTAxPPfWUy3Y7b0swFRYWNuD32cfHh4aGhnqtda9+jVVKxQL5wHkgTmttbbfPH6O7oQLCtdZ1tyjHF7gGWIGRWuuadvtMtmvE2K5R4MhrDyau+T9Y9IvW1lays7PZu3cvdXUd//8qpUhISCAtLY3Ro0c7qYZiIIwbN46XX36Zbdu2cfjwYcDI9Pj+++8zY8YM0tPT8fLyctj1zlyt4YOsYtZ/cQn3uis8Ys7kX9z3Em8q7uJoBePvgTlfgQn3gcl1ktDU1dWxY8cO+/pdd93l1OBMCCGGu7i4OJYtW8b69esBOH/+POvWrWPlypUuOSRjz5497NmzhwkTJhATEzPY5oxdbFtuax8gAWita5RSGcB9wDxgR+eT20kBvG3ldBjLoLW2KqW2AS8Ci4C2bo6OuvagIQHaMGIymTh06FCH4MzNzY2ZM2eSkpJCSEiIE2snBpKnpyePPPIIkyZNYuPGjfaMhEePHqWwsJDly5f3aV6vqoYWNh2/wgfZxRQXF/GA+RC/MWeS7JXb9QlBUTD9SZixCoJjen3d/rR9+3b75OzBwcGkpaU5uUZCCCGmT59OTU2Nvfv5qVOn2Lp1K+np6S41PKOkpIR9+/YBcPbsWXJycpwxhtlLKXW4qx1a69tVpq3Jr4vMXQCcxQiSJnLrIKkn5WArx9HXHjQkQBtGTCYTKSkpbNq0CU9PT1JSUpgzZ86Ajj0SrmXixIl87WtfY/PmzeTk5ADGFAt//vOfSUlJYfHixT2efLy51cquvFI+PnqJw6fPsVBn8W1TJqmeJzF3HlcG4O4DicthxpMQnea0pB89UVxcbM+ECfDAAw/IpOxCCOEi0tLSqKmpsc9PefDgQfz9/bnrrrucXDODxWJh48aN9q6YYWFhzJw508m1umNtGViqutnftj2oH8px1LUHDQnQhpkZM2ZQWlpKTEwMkydPdnZ1hAvw8fFh5cqVxMfHs2nTJvu8aZmZmZw7d44vfelLjBw5sstztdYcLqpg/ReXOHr8KPOaD/CMOZtfmfO6DMq0MqHGLYCpj0HiMvB0nTT/3bFarfZxZ2CMD5k4ceItzhBCCDGQlFLcf//91NTUcOrUKcDo9eDv7+8SE1kfOHCAy5cvA8aP5cnJyc7qgtnYg5ay3mprruxrcovelOOoa7sMCdCGGXd3d8aPH+/saggXNGXKFKKioti4cSPnzp0D4Nq1a/z+979n4cKFpKWlYTab0VpztLiSzccvUXA8g2n1B3jKlM1PTBegi0YljUJFpcCUL6ESl7lMwo+eys7OtifTcXNzIz29c2IpIYQQzmYymVixYgV1dXUUFRUBxkTWvr6+Tv3eU1ZWxueff25fnzJlCgEBAU6rTx+0tVJ1N5dBQKfjHFmOo649aEiAJoSwCwgIYPXq1WRnZ7Nt2zZaWlqwWq3s3LmTozmnaQ6No+7cXqY2ZvOPpuOEqeou30U0CjU2GRIeQU1eAYGDM/FMbW0tO3futK/Pnz9fEoMIIYSLcnd354knnuCtt96itLTUPpH1qlWriI2NHfD6WK1WNm7cSGtrKwCRkZEkJCQMeD0cJM+27K4LyQTbsrtxYn0px1HXHjRcd9CHEMIplFLMmTOHF776IoGhN1q7ykuv0Hjqc9JbdrHcvM8IztqxmjzQE+6HR15HfecMfGUrpL46aIMz6JgYJCQkhNTUVCfXSAghxK20TWTdNml1S0sL7777LmfODPx39yNHjthb85RSLF261CWzS/ZQWzPgfbZ0+Ha2VPdpQANw4DblHLAdl2Y7r305JoxkH+2v58hrDxqD9n+JEMLx6hqa2L97G5+88b8o+M2XePH6D1lMBiYsALQqdz5lEW/zKBUE0OwZimXqE/DYnzH97wLU6g9g9jODrhtjVy5cuMDRo0ft65IYRAghBoeAgACefvppe1dCi8XC2rVrOXny5IDVoaqqis8++8y+npaWxqhRowbs+o6mtc4HtmHMUfZKp90/AnyBt9vPQ6aUildKxXcqpxb4i+34H3Yq51Vb+Vvb5kDr7bUHO+niKMQwppvruXx6P1eO7cT90kFiG0+SqhpuHKBgAYeYQCHrSaeUMADOE8Vv3V/kvnvSmZ2UBC6UytgRampq+Oijj+zr8fHxTJgw4RZnCCGEcCVhYWE899xzvP3221RUVGC1Wvnwww9paWlhxowZ/XptrTWbNm2iqakJgNDQUO6+++5+veYA+RqwH3hdKbUEOA0kY8xZdgb4t07Hn7YtO39J+C6wEPiWUmoGcAhIAJYBpdwchPXm2oOaBGhCDCfVV2g8f4CrpzJQxQeIrDvNaFqxd0LsIs4q8xyDiprP84l3s++qNxkHD6O1prnFwiebNnE6N5elS5fau5MMds3Nzaxdu5aqKmOssYeHhyQGEUKIQSg4ONgepF2/fh2tNR9//DGtra0kJSX123VzcnI6dKlcunTpkOiBobXOV0olAT8G0oEHgSvA68CPtNblPSynTCmVAvwAWA7MB8qAt4Dva60v9te1BwsJ0IQYolRLHV4VeVhKP6XqXCbuV47g31yKFxB9i/OuqVCuhc0lIPEeRs+8j9CgKPu+e4D4KTNYv349ZWVlAOTn5/PGG2+wZMkS5syZM5j712O1Wvn444+5dOkSYIwZWLlyJUFBQ2ZqFSGEGFYCAgJ49tln+ctf/sLVq1cB+OSTT2hqaiI1NdXhk1mfO3eOTz75xL6elJREdPStPnUHF611MfBcD4/t9h/XFlB9w/Zw+LUHOwnQhBgKGiqh5DhcOYb10hc0F3/BhOpClG1KkJBbnFqgR3EpYAZu49KIm30P4VGTGHGLD6wxY8bw0ksvsXPnTjIzMwGj1enTTz/l+PHjPPLII0RGRjry1Q2YnTt32ufQAUhPT5c5z4QQYpDz8/PjmWee4Z133rHPR/bZZ59RVFTEI488gr+/Y+bkzMrKYvPmzWhtfPYGBARwzz33OKRsMbxIgCbEYGK1QFk+XM2Bqyfh6kmsV3MwVRXbDzEBXt2cXq89OaHHccE7EdPYOUTNWMz0+InEut1Zq5e7uzv3338/CQkJbNy4kevXrwNw6dIl3nzzTVJTU7n77rsHVZeOI0eOsG/fPvt6cnIyycnJTqyREEIIR/Hx8eHLX/4y7733HhcuXADgzJkzvPHGGzz44INMnTq1161pFouFbdu2cfDgQfu2gIAAnnzySby8uvtEFqJ7EqAJ4YosrVBRCNdybY88uJaLvn4W1drY4dDuQqtWbeKsHs0JayyFXol4xcwlbnIS8yZEkOzn6ZBqRkVF8dJLL7Fv3z727t2LxWLBarWyb98+Tp48yUMPPTQoJkYvKCjo0CVlwoQJ3H///U6skRBCCEfz8vLiqaeeYvv27Rw6dAiAxsZG1q1bx8mTJ3n44YfvuDWtsbGRDz/8kHPnztm3jRo1ilWrVjmsZU4MPxKgCeEsWkPddSg7Z3ucNVrHys5BeQFYmm86pbvf9pq1mbN6DCes48jR4yj1i8ccGkf8yCCWpSTyWKiPw/vZt3Fzc2PhwoVMnjyZv//97/ZfJisqKnjnnXeYMGEC9957L+Hhrpl6/9q1a3zwwQdYrVYAIiIiWLly5aAeSyeEEKJrHh4ePPjggyQkJLBhwwYqKysByMvL48KFC9x3330kJCT0qOWrvLyctWvXUlpaat+WmJjI8uXL8fDw6LfXIIY+1dZPVgwspVSdt7e3T319/YBfOy/PmJB90qRJA37tYcfSAtWXoOI8lBcarWLlhcZ6xXloqr5NATcr0cHkWqPI1VGcto4lV0dhCpvAjHHhJI8LZc64EEYHeTvlPlutVo4cOcJnn31mTy8MRrKN2bNns3DhQvz8/AasPrdz5swZ1q9fT0ODMbWAn58fX/3qVwdNRkr5Wx4e5D4PD3KfB15TUxOfffYZ2dnZHbYrpRgzZgyxsbHExcUxevRozGYzVVVVFBUVUVRUxIULF7h27VqH8+bPn8+iRYtu+QOfs+6zj48PDQ0N9Vpr3wG9sOgVaUEToi+a66DqElQVG4FYZTFUXjDWKy8Y27S1V0Vf0SGctY7mnB7NWT3a/tzqFcyMccHMigri0ahgpo8NItDbNcZ6mUwmkpKSmDRpEjt37uSLL74AjDlhsrOzOXHiBPPnzyc5Odmp49MsFgs7d+4kIyPDvs3d3Z0nn3xy0ARnQggh+sbT05OHH36YxMRENmzYYJ9eRWtNcXExxcXF7N69Gw8PD7y9ve37OzOZTCxdurTf51cTw4cEaEJ0xWqF+jKouQI1JVBz2ba8AtVXjMCr6iI0VvbpMrXai0IdSYEeZSytIynUIynUkdTig6+HmcmjA5k6JpCnRgcyZXQgsWG+mEyuPTG0v78/y5YtIzk5ma1bt1JYWAgYv1Zu376dgwcPkpycTFJS0oAPoK6qquLDDz+kuPhGYpWAgAAee+wxRo0aNaB1EUII4XyxsbG8/PLLZGZmkpeXR0lJSYf9zc3NNDffPOzAZDIxZswY7rnnHqKiom7aL0RvDckATSk1hhsT2YViTGT3McZEdhV3UE4I8H2MSfRGYkyit4VuJtETLs5qgYYKqC2Fumu2x3WoK4Xaq8Z2+7IUtMUhly3RwVzUIyjS4VywRlCkI7igwynSEZQRQNvIsnB/TxJGBpA60p+vRAYwZXQA48L8MLt4MHYrkZGRfPnLX+bs2bNs27bNnu2xpqaG7du3s2fPHmbPns28efMGpOXq7NmzrF+/nvZdi8ePH8+KFSvw9ZVeH0IIMVx5eXmxaNEiFi1aRF1dHQUFBRQUFJCfn091tTEcwd3dnbFjxxIVFUV0dDSjR4+WsWaiXwy5AE0pFQfsB8KBDUAuMBdjIrx0pVSa1rqsB+WE2sqZCOwE1gLxGBPkPaSUStFaF/TPqxC31dpstF7VlxtBV0PbssLYVl9me7Q9v27s62V3w+40aTdKdAhXCOWyDuWKDqFYh3NRj+CiDuOyDqOZjl35gnzcmRDux33hfowP9ych0p9Jkf6EOiizoqtRSjFx4kTi4uI4fPgwe/bsoba2FjB+lczMzOTgwYNMnjyZ5ORkRo8e7fCEJleuXCErK4sjR450qNfixYtJS0uThCBCCCHsfH19mTp1KlOnTkVrTXl5OS0tLYwYMQKz2ezs6olhYMgFaMBvMIKz17TWv2rbqJT6GfBN4CfASz0o5z8xgrOfa62/1a6c14Bf2q6T7sB6Dx9WKzTXQlNNu0cVNFYbSTPaLxurbI9KY9lQaTxv6f/kKlXahxIdwlUdTCnBlOhg47kO5ooO4bIOowx/dBeJ7j3MJqLCfFgQ6kN0qC/jwnwZH+7H+HA/Qn09+i2joiszm83MnTuXWbNmcfz4cfbv329vUbNarZw4cYITJ04QEBDApEmTiI+PJzo6Gje33r1NNTc3c/LkSbKzs7l06VKHfX5+fqxcuZKYmJi+viwhhBBDmFKK0NBQZ1dDDDNDKkBTSsUC9wHngTc67f4B8CLwtFLq21rruluU4ws8DdTZzmvv1xiB3v1Kqdgh3YpmaTUCodZGY9lcDy0N0FJne257NNfdeLTUG8FX23pTLTTXtHtuezhJhfajTAdQRgDXdQBlOpBy/CnVwVzTgVzTQZTqIK4TeFPLV2fh/p7MDPZmbIgPY4K9GRPsw9hgH2LCfBgZ6D2ouyb2Jzc3N2bNmsWMGTM4d+4cGRkZFBUV2fdXV1eTlZVFVlYWnp6eTJgwgdjYWIKDgwkKCiIgIOCmXzC11jQ2NlJdXU1VVRXnzp3j2LFjHTJJtomLi2PFihUulU1SCCGEEKLNkArQgMW25TatO/Zl01rXKKUyMAK4ecCOW5STAnjbyqnpVI5VKbUNI9hbBAyqAO3Auz+C4oN46GZOm6y462bcdRPuugkPq/HcQzfhbm3CjVZnV7dbrdpENT5UaH8q8aNS+91Yal/KCaBc+1OBv7HU/lTgR2sP/su7mxUj/DwJ8/ckMsCLkYFeRAQay8gAbyJtz73cpZtDX5hMJiZOnMjEiRO5dOkShw4dIi8vj8bGGxNxNzU1kZOTQ05Ojn2bUgp/f3+CgoJwd3e3B2VdDeBuYzabSUhIICkpiejo6GHZgimEEEKIwWGoBWhtk0qc6Wb/WYwAbSK3DtB6Ug62cm5JKXW4m11eWmv7fBgDxXxhP3OaDgzoNbtSq72oxZta7W1belGNLzXahxq8qdE+VONDDT5Uax+qtB/V+FClfanClzq86H7a5o683RR+nmbGepgI9DIT4Gk2ll4mAj3NBHiZCfY2E+LtRpC3GX8PUxdf4C1AHbTW0VwGRbcdxeh8bd0HB4vExETi4+O5du0aFy9e5NKlS9TV3dzQrbWmurraPmj7Vvz8/Bg/fjzjxo3Dy8uLpqYmzpzp7s968Bls91j0jtzn4UHu8/DgrPss8x4PLkMtQGtLA9f1RBU3tgcNUDkup0X1PBGFVSsa8KABTxrxoEF7Uo8nDXjSoD1sz72o0zeW9XhSjxf12pM6vKnDizrtRR1e1Gpv6jGeW7sYt+VuAnezCU83hYdZ4W5WuJsUXm4KTzcTgW6KCDdjv5ebCS83hY+HCR93E97uJnxtSx93E36eJvw8zPh5mKSr4SBiMpmIiIggIiKCWbNmUVlZyaVLl6iurqauro66ujr7pNKdmc1mfHx88PHxwc/Pj6ioKCIiIqS1TAghhBCDylAL0G6n7ZtaX39G6HE5WuvZXRagVJ1SymegZ5LPXfx1dpyZj8XkSeCISKxmLywmLyxmT6xmT6xuXljMXljN3miTOyhF2/dbpRQKMNm2eSvwQTHCpDArhUmByaQw2Z67mU2YlcJsUriZjaVZKTzcTLiZFR5mE+72h5Iv0v1koP+P9bfW1laqqqqoqqqipaWFgIAAAgMD8fb2Hrb/h4baPRZdk/s8PMh9Hh4G+j4P18/HwWqoBWhtLVvdTagU0Om4/i7H5cTPvRcVaEymKB8CYjByc3MjNDRUsmoJIYQQYkgaapP/tA3o6m5s2ATb8naDUBxVjhBCCCGEEEL02FAL0D63Le9TSnV4bUopfyANaABulyXjgO24NNt57csxYSQaaX89IYQQQgghhOizIRWgaa3zgW1ADPBKp90/AnyBt9vPgaaUildKxXcqpxb4i+34H3Yq51Vb+VuH9BxoQgghhBBCiAE31MagAXwN2A+8rpRaApwGkjHmLDsD/Fun40/blp1HT34XWAh8Syk1AzgEJADLgFJuDgCFEEIIIYQQok+GVAsa2FvRkoA/YQRm3wbigNeBFK11j2awsh2XYjtvvK2cZOAtYLbtOkIIIYQQQgjhMEOxBQ2tdTHwXA+P7TbvqNa6HPiG7SGEEEIIIYQQ/WrItaAJIYQQQgghxGAlAZoQQgghhBBCuAgJ0IQQQgghhBDCRUiAJoQQQgghhBAuQgI0IYQQQgghhHAREqAJIYQQQgghhIuQAE0IIYQQQgghXIQEaEIIIYQQQgjhIiRAE0IIIYQQQggXIQGaEEIIIYQQQrgIpbV2dh2GJaWUFVDe3t4Dfu22e66UGvBri4Ej93nok3s8PMh9Hh7kPg8PzrrPDQ0NtstraZwZBCRAcxKlVAtgBhqccHkv27LRCdcWA0fu89An93h4kPs8PMh9Hh6cdZ+9AYvW2n2Aryt6QQK0YUgpdRhAaz3b2XUR/Ufu89An93h4kPs8PMh9Hh7kPouekGZOIYQQQgghhHAREqAJIYQQQgghhIuQAE0IIYQQQgghXIQEaEIIIYQQQgjhIiRAE0IIIYQQQggXIVkchRBCCCGEEMJFSAuaEEIIIYQQQrgICdCEEEIIIYQQwkVIgCaEEEIIIYQQLkICNCGEEEIIIYRwERKgCSGEEEIIIYSLkABNCCGEEEIIIVyEBGhCCCGEEEII4SIkQBsClFJjlFJrlFKXlVJNSqnzSqlfKKWC77CcENt5523lXLaVO6a/6i56rq/3WSnlq5RarZR6TymVq5SqU0rVKKWylVLfVkp59PdrELfnqL/nTmUuUEpZlFJaKfUfjqyv6B1H3mel1FSl1NtKqWJbWaVKqd1KqS/3R91Fzzjws/kupdQG2/mNSqkLSqnNSqn0/qq76Bml1Eql1K+UUnuVUtW299h3elmWw9/7xeAlE1UPckqpOGA/EA5sAHKBucAiIA9I01qX9aCcUFs5E4GdQBYQDywDSoEUrXVBf7wGcXuOuM+2D/NPgXLgc+AcEAI8AkTayl+itW7sp5chbsNRf8+dyvQHjgNhgB/wE6319xxZb3FnHHmflVLPAn8A6oFPgPNAEDAFuKy1fsLB1Rc94MDP5peB3wB1wHrgIjAG+BLgA3xPa/2T/ngN4vaUUkeB6UAtxr2JB97VWj91h+U4/L1fDHJaa3kM4gewFdDA1ztt/5lt+//0sJzf2Y7/Waftr9m2b3H2ax3OD0fcZ2AGsBrw6LTdHzhsK+fbzn6tw/nhqL/nTueuwQjKv2sr4z+c/TqH+8OB79vzgFbgKBDZxX53Z7/W4fpw0Hu2O1AJNACTOu1LABoxAnNPZ7/e4frACKAmAApYaLu37zjj/4s8htZDWtAGMaVULJCP8YtpnNba2m6fP3AF400jXGtdd4tyfIFrgBUYqbWuabfPZLtGjO0a0oo2wBx1n29zjSeBd4FPtNaP9LnS4o71x31WSi0DPgaeBtyAt5AWNKdy5H1WSu0B5gNTtdY5/VZpcUcc+NkcAZQAx7XW07vYfxyYCoRpaV1xOqXUQozeKXfUgjYQn/Fi8JExaIPbYttyW/s/aABbkJWB0QVi3m3KSQG8gYz2wZmtHCuwzba6qM81Fr3hqPt8Ky22ZWsfyhB949D7rJQKB34PfKy17tWYCNEvHHKfbWOD5wPZwEml1CKl1Hds40mX2H5cE87hqL/lUowfTycqpSa036GUmojRcnNUgrOkjhv1AAAFU0lEQVRBbyA+48UgI2/gg9sk2/JMN/vP2pYTB6gc0T8G4v48b1tu6UMZom8cfZ/fxHiPf6kvlRIO56j7PKfd8Tttj/8L/BewHTiqlBrfh3qK3nPIPdZGF6dXMP6ODyul/qyU+n+VUm9jdEs/CTzmgPoK55LvYOImbs6ugOiTQNuyqpv9bduDBqgc0T/69f4opV4F0jHGsazpTRnCIRx2n5VSz2Mk+Hlca33VAXUTjuOo+xxuW/4DcB0jacQOYATwA4xurZuUUlO11s29r67oBYf9LWut/6aUugy8D7TPynkVo8uyDDsY/OQ7mLiJtKANbcq27OtAQ0eVI/pHr++PUupLwC8wxjk8qrVuuc0pwnl6dJ+VUjEY9/RvWusP+rlOwvF6+vdsbrd8QWu9XmtdrbXOB57B6Po4EXi0f6op+qDH79lKqacwWkT3YiQG8bEtdwC/Btb2Ux2F65DvYMOQBGiDW9uvKoHd7A/odFx/lyP6R7/cH6XUcowP91JgoSSAcTpH3ec1GFnfvuaISgmHc9R9rrAtm4DN7XfYusZtsK3OvdMKij5zyD22jTNbg9GV8Wmtda7WukFrnYvRQnoYeMyWnEIMXvIdTNxEArTBLc+27K5fctug4u76NTu6HNE/HH5/lFKPAX/D6CZzt9Y67zaniP7nqPs8C6P72zXbpKlaKaUxukMB/Jtt28d9q67oJUe/b9d0Tixg0xbAed9B3YRjOOoe34eRan93F8kjrMAe2+rs3lRSuAz5DiZuImPQBrfPbcv7lFKmLlKzpmH8kn7gNuUcsB2XppTy7yLN/n2dricGlqPuc9s5TwJvA5eARdJy5jIcdZ/fxugG1dkEYAHGWMPDwBd9rrHoDUfd5+MYY8/ClFIRXYw1nGJbnu97lcUdctQ99rQtR3Szv227jDEc3Bz6GS+GBmlBG8RsYw22YcxR9kqn3T8CfIG328+boZSKV0rFdyqnFviL7fgfdirnVVv5W+WLvHM46j7btj+Dca8vAAvknroOB/49v6a1fqHzgxstaJts297otxcjuuXA+9wK/M62+tP2afWVUlOBZzGmzfjQwS9B3IYD37P32pYrlVLT2u9QSs0AVmKMS9rpuNqL/qKUcrfd57j223vz/0UMfTJR9SBn+0Pfj9GlaQNwGkjGmLPsDJDafo4UW1cntNaqUzmhtnImYrzZH8IYiLwMY4xSqu1NRDiBI+6zUmoRxmBzE8a4huIuLlWptf5FP70McRuO+nvupuxnkYmqXYID37d9MJJFzMNoEd2F0aryKEbXxm9rrX/Wzy9HdMGB93gN8BxGK9l6oAjji/xywAP4hdb6m/38ckQ3bGO5l9tWI4H7MTJrtgXX17XW37EdGwMUAkVa65hO5dzR/xcx9EmANgQopcYCP8ZIlR6KMev8x8CPtNblnY7t9gudUioEIz3zcmAkUAZ8Cnxfa32xP1+DuL2+3ud2X9Bv5aYPDjGwHPX33EW5zyIBmstw4Pu2D/DPwBPAOKARyAL+W2v9aX++BnFrjrjHSimFkZXzWWA64A9UYwTkv9daSxZHJ1JK/RDje1N37J+ptwrQbPt7/P9FDH0SoAkhhBBCCCGEi5AxaEIIIYQQQgjhIiRAE0IIIYQQQggXIQGaEEIIIYQQQrgICdCEEEIIIYQQwkVIgCaEEEIIIYQQLkICNCGEEEIIIYRwERKgCSGEEEIIIYSLkABNCCGEEEIIIVyEBGhCCCGEEP9/+3UsAAAAADDI33oaO8oigAlBAwAAmBA0AACACUEDAACYEDQAAIAJQQMAAJgQNAAAgAlBAwAAmBA0AACAiQDPyRsoJl2gpQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 436
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax2 = ax.twinx()\n",
    "ax.plot(zrange, p.cdf(zrange))\n",
    "ax.plot(zrange, empirical_cdf)\n",
    "ax2.plot(zrange, empirical_cdf - p.cdf(zrange), c=\"tab:gray\")\n",
    "ax.grid(alpha=0.6)\n",
    "ax2.set_ylabel(\"diff\", fontsize=13);\n",
    "ax.set_ylabel(\"P(x) || Q(x)\", fontsize=13);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling from $q(z)$\n",
    "\n",
    "if $y\\sim\\text{U}(0, 1)$, then\n",
    "\n",
    "$$\n",
    "    z = \\frac{1}{\\lambda_n}\\log\\left(\\frac{Z_q\\lambda_n\\exp(\\lambda_nz_n)(y - I_{i_{n-1}})}{p(z_n)} + \\exp\\big(\\lambda_ni_{n-1}\\big)\\right)\n",
    "$$\n",
    "\n",
    "Where\n",
    "* $I_{i_{n-1}} = P(z \\leq i_{n-1})$\n",
    "* $Z_q$ is the normalization coefficient for the $q$ distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_cdf_nonorm(x, f, z_obs, lb, ub):\n",
    "    \"\"\"\n",
    "    Parameters\n",
    "    ----------\n",
    "    intersections: list\n",
    "        Set of intersecting points\n",
    "    lb: float\n",
    "        Lower bound of the distribution\n",
    "    ub: float\n",
    "        Upper bound of the distribution\n",
    "    \"\"\"\n",
    "    intersections = [compute_intersect(z1, z2, p.logpdf) for z1, z2 in zip(z_obs[:-1], z_obs[1:])]\n",
    "    regions = np.array([lb] + intersections + [ub])\n",
    "    \n",
    "    if x <= lb:\n",
    "        return 0\n",
    "    else:\n",
    "        I = 0\n",
    "        bounds = regions[x >= regions]\n",
    "        pair_bounds = list(zip(bounds[:-1], bounds[1:]))\n",
    "        for ix, (b0, b1) in enumerate(pair_bounds):\n",
    "            ln = finite_approx(p.logpdf, z_obs[ix])\n",
    "            I += (f(b1) - f(b0)) / ln\n",
    "        if len(pair_bounds) == 0:\n",
    "            ix = -1\n",
    "        if x < ub:\n",
    "            ln = finite_approx(p.logpdf, z_obs[ix + 1])\n",
    "            I += (f(x) - f(bounds[-1])) / ln\n",
    "        return I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_norm = q_cdf_nonorm(1, f_approx, z, 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_q_cdf(f, z_obs, lb, ub):\n",
    "    Z_norm = q_cdf_nonorm(ub, f, z_obs, lb, ub)\n",
    "    def q(x):\n",
    "        return q_cdf_nonorm(x, f, z_obs, lb, ub) / Z_norm\n",
    "    return q\n",
    "    \n",
    "q_cdf = make_q_cdf(f_approx, z, 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf = [q_cdf(zi) for zi in zrange]\n",
    "\n",
    "plt.plot(zrange, cdf)\n",
    "plt.grid(alpha=0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "lb, ub = 0, 1\n",
    "regions = np.array([lb] + intersections + [ub])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_inv(y, z_obs, logp, regions, Z_norm):\n",
    "    \"\"\"\n",
    "    Parameters\n",
    "    ----------\n",
    "    y: float\n",
    "        random variable from a U(0, 1) distribution\n",
    "    \"\"\"\n",
    "    i0 = regions[y >= regions].max()\n",
    "    c = q_cdf(i0)\n",
    "\n",
    "    if y <= z_obs.min():\n",
    "        zn = z_obs[0]\n",
    "    elif y >= z_obs.max():\n",
    "        zn = z_obs[-1]\n",
    "    else:\n",
    "        # find intermediate points\n",
    "        z1 = z_obs[y >= z_obs].max()\n",
    "        z2 = z_obs[y <= z_obs].min()\n",
    "\n",
    "        intersect = compute_intersect(z1, z2, logp)\n",
    "\n",
    "        if y < intersect:\n",
    "            zn = z1\n",
    "        else:\n",
    "            zn = z2\n",
    "\n",
    "    ln = finite_approx(p.logpdf, zn)\n",
    "    z_samp = np.log(ln * Z_norm * (y - c) * np.exp(ln * zn) / p.pdf(zn) + np.exp(ln * i0)) / ln\n",
    "    return z_samp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.1 s, sys: 140 ms, total: 9.24 s\n",
      "Wall time: 9.22 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "yvals = random_sample(1_000)\n",
    "z_samples = []\n",
    "for y in yvals:\n",
    "    z_samp = q_inv(y, z, p.logpdf, regions, Z_norm)\n",
    "    z_samples.append(z_samp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 373
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(z_samples, label=\"sampled histogram\")\n",
    "plt.plot(xrange, q_dist(xrange), linewidth=2, label=\"$q(z)$\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc9acaf7110>]"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "inv_cdf = [q_inv(y, z, p.logpdf, regions, Z_norm) for y in zrange]\n",
    "plt.plot(zrange, inv_cdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# All together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(271)\n",
    "lb, ub = 0, 1\n",
    "z_obs = np.sort(p.rvs(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_f_approx = f_approx_gen(z_obs, p.logpdf)\n",
    "def f_approx(x): return np.exp(log_f_approx(x))\n",
    "\n",
    "Z_norm = q_cdf_nonorm(1, f_approx, z_obs, 0, 1)\n",
    "q_cdf = make_q_cdf(f_approx, z_obs, 0, 1)\n",
    "cdf = [q_cdf(zi) for zi in zrange]\n",
    "\n",
    "intersections = [compute_intersect(z1, z2, p.logpdf) for z1, z2 in zip(z_obs[:-1], z_obs[1:])]\n",
    "regions = np.array([lb] + intersections + [ub])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 697
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "ax[0].scatter(z_obs, p.pdf(z_obs), color=\"tab:gray\")\n",
    "ax[0].plot(xrange, f_approx(xrange), label=\"$f_z(z)$\")\n",
    "ax[1].plot(zrange, cdf, label=\"$F_z(z)$\")\n",
    "\n",
    "for axi in ax:\n",
    "    axi.grid(alpha=0.6)\n",
    "    axi.legend(fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 7.58 s, sys: 89.8 ms, total: 7.67 s\n",
      "Wall time: 7.64 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "yvals = random_sample(1_000)\n",
    "z_samples = []\n",
    "for y in yvals:\n",
    "    z_samp = q_inv(y, z_obs, p.logpdf, regions, Z_norm)\n",
    "    z_samples.append(z_samp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(z_samples, label=\"sampled histogram\")\n",
    "plt.plot(xrange, q_dist(xrange), linewidth=2, label=\"$q(z)$\")\n",
    "plt.legend();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
